Answers
The value of c is 20.35 (approx).
What is Pythagorean Theorem?The Pythagorean Theorem states that the hypotenuse, or side opposite the right angle, of a right triangle, which is represented by the square, is equal to the sum of the squares on the legs of the triangle (or, in popular algebraic notation, a2 + b2 = c2).
Where is the Pythagorean theorem used?The following are some significant applications of the Pythagorean theorem in daily life: used in architecture and building, used to determine the shortest distance in two-dimensional navigation. used to measure how steep a mountain's or hill's slope is.
Let the other 2 sides of the triangle be named a and b
Given:- a = 15.5ft
b = 13.2ft
According to the Pythagorean Theorem, We know that
[tex]a^{2}+b^{2}=c^{2}[/tex]
By substituting the values of a and b we get
[tex]15.5^{2}+13.2^{2}=c^{2}[/tex]
[tex]c^{2}= 414.5\\c=\sqrt{414.5}\\ c=20.35[/tex]
c is the hypotenuse of the triangle.
Hence the value of c is 20.35
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Related Questions
A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top. Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
A) What are the dimensions of the square to be cut from each corner?
B) What would the volume be of the open box?
Answers
Dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
What is Three dimensional shape?Three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top
Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
Let the cut squares will have side h then h is the height of the box and the two lengths are (25-2h) and (20-2h).
The dimensions of the box are (25-2h) and (20-2h)..
Volume of the box will be V=h(25-2h)(20-2h)
Hence, dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
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Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answers
Answer:
See below.
Step-by-step explanation:
Let the price of drinks be x and the price of candies be y.
Condition # 1:9x + 4y = 60 --------------------(1)
Condition # 2:10x + 2y = 57.50 --------------(2)
Multiply Eq. (2) by 22(10x + 2y) = 57.50*2
20x + 4y = 115 --------------(3)
Subtract Eq. (3) from (1)9x + 4y - 20x - 4y = 60 - 115
9x - 20x = -55
-11x = -55
11x = 55
Divide both sides by 11x = 55/11
x = $5Put x = 5 in Eq. (1)
9(5) + 4y = 60
45 + 4y = 60
Subtract 45 to both sides4y = 60 - 45
4y = 15
Divide both sides by 4y = 15/4
y = $3.75So, the cost of one drink is $5 and the cost of one candy is $3.75.
[tex]\rule[225]{225}{2}[/tex]
What is the converse of the following conditional statement?
"If this month is September, then next month ends in the letter r."
Determine the validity of the converse and give a counterexample if the converse is not valid.
Answers
The converse statement is:
"If next month ends in the letter r, then this month is September."
And a counterexample of this is the month of September.
What is the converse of the conditional statement?A conditional statement is of the form:
If P, then Q.
And a converse statement of the above one will be:
if Q, then P.
Here our conditional statement is:
"If this month is September, then next month ends in the letter r."
So we have:
P = this month is September.
Q = The next month ends in the letter r.
Replacing that in the converse statement formula we get:
"If next month ends in the letter r, then this month is September."
A counterexample is September, it ends with an r, and the month after it is not September.
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Answer:
If next month ends in the letter r, then this month is September. The converse is invalid; a counterexample is December.
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: m
Answers
The value of angle A and B are 60° and 120° respectively.
How to calculate the angles?It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.
Therefore A = D
B = C
When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:
ABK = 30°
Also, KBC = 90°
Therefore, B = 30° + 90° = 120°
A = D = 180° - 120° = 60°
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Complete question:
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: mA and mB.
-2(7+3m) +6m>3 (3m-5)
Answers
Answer:
1/9 > m
Step-by-step explanation:
-2(7+3m)+6m>3(3m-5)
Distribute.
-14-6m+6m>9m-15
Combine like terms.
-14>9m-15
1>9m
Get m to be alone.
1/9>m
Question :
-2(7+3m) + 6m > 3(3m-5)
-2(3m+7) + 6m > 3(3m-5)
-6m - 14 + 6m > 9m - 15
Next, let we combine it
-14 > 9m - 15
After that, let add 15 to both sides
-14 + 15 > 9m - 15 + 15
1 > 9mNext, we will divide both sides by the same factor
1/9 > 9m/9Lastly we will cancel the terms that are both in the numerator and denominatorMove the variable to the left and flip the inequality
m < 1/9
The final answer is m < 1/9
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over the past month, george the tortoise has been flipped onto his back 146 times by angie the tortoise. george has been able to get back on his feet without help 3 times. what's the empirical probability that george will be able to get back on his feet without help the next time angie flips him over?
Answers
The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
Describe the term empirical probability?The likelihood of an event is closely related to an empirical probability, also described as an experimental probability. Empirical probability bases its evaluation of the likelihood that a specific result will recur on the number of instances of that outcome together within sample set.For the given question.
We include George the turtle, who Angie has successfully turned over 146 times the turtle.3 times George has used the assistance to get back up on his feet. The empirical probability is really what we seek.Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.
empirical probability = 3/146
Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
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f(x) = (1 + =)",
k, n EN,
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x),
(a) prove that n = 6k + 2.
Given also that the coefficients of x4 and x5 are equal and non-zero,
(b) form another equation in n and k and hence show that k = 2 and n = 14.
Using these values of k and n,
(c) expand f(x) in ascending powers of x, up to and including the term in x5.
Give each coefficient as an exact fraction in its lowest terms
n>2
Answers
Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x)
(a) It is proved that n = 6k + 2
(b)k = 2 and n=14
(c) After expansion, the equation is
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
What is the binomial theorem?
The algebraic expansion of a binomial's powers is described by the binomial theorem (also known as binomial expansion) in elementary algebra.
The theorem states that the polynomial (x + y)n can be expanded into a sum including terms of the form axbyc, where the exponents b and c are nonnegative integers and b + c = n, and the coefficient an of each term is a particular positive integer dependent on n and b.
Solution Explained:
f(x)= (1+x/k)^n
Given that the coefficient of x^3 is twice the coefficient of x^2 in the binomial expansion of f(x)
a)
Coeff of x^3 = 1/6[n(n-1)(n-2)/k3]
Coeff of x^2 = 1/2[n(n-1)/k2]
1/6[n(n-1)(n-2)/k3] = 2* 1/2[n(n-1)/k2]
Canceling on both sides gives:
(n-2)/(6k) = 1
n = 6k+2 Hence proved
Given also that the coefficients of x^4 and x^5 are equal and non-zero,
b)
Coeff x^4 = 1/24 [n(n-1)(n-2)(n-3)/k4
Coeff x^5 = 1/120 [n(n-1)(n-2)(n-3)(n-4)/k5
1/120 [n(n-1)(n-2)(n-3)(n-4)/k5 = 1/24 [n(n-1)(n-2)(n-3)/k4
Canceling gives:
(n-4)/(120k) = 1/24
n = 5k+4
From previous:
n = 6k+2 = 5k+4
k = 2
n=14
Using these values of k and n,
c)
Give each coefficient as an exact fraction in its lowest terms
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5
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I WILL MARK BRANLIEST FOR CORRECT ANSWER! The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who use a mobile device in a traditional class?
23%
37%
46%
72%
Answers
The joint relative frequency is 23%. So option (1) is correct.
Joint relative frequency is defined as the ratio of a frequency that is not in the total row or column to the total number of values or observations. The marginal frequency in a two-way frequency table is the entry in the "total" for the column and the "total" for the row.
Given data:
Traditional Online Row totals
Computer: 28 62 90
Mobile device: 46 64 110
Column totals: 74 126 200
The joint relative frequency can be found by the formula:
= (Number of students using a mobile device in traditional class / Total Number of students) x 100%
Number of students using mobile devices in traditional class = 46
Total number of students = 200
= (46 / 200) x 100%
= 0.23 x 100%
= 23 %
Therefore the joint relative frequency of students in traditional classes using a mobile device is 23%.
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After raining for 3/4 of an hour, a rain gauge is of 2/5 the way full. If it continues to rain at the same rate for 15 more minutes, what fraction of the rain gauge will be filled?
Answers
Answer:
8/15
Step-by-step explanation:
You want the fraction of a rain gauge filled after 15 more minutes when the rain rate is 2/5 of the gauge in 3/4 of an hour.
Proportion15 minutes is 1/4 hour, so 15 more minutes brings the total time to 1 hour. The fraction (x) of the gauge that is filled will be ...
x/1 = (2/5)/(3/4)
x = (2/5)(4/3) = 8/15
After a total of 1 hour, the rain gauge will be 8/15 of the way full.
the human resources department at a major high-tech company recently conducted an employee satisfaction survey of 100 of its 3000 employees. data were collected on such variables as age, gender, marital status, current salary, level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title. which of the variables listed are considered to be ratio level data?
Answers
Gender and marital status and Job title.
What are edtech companies?Computer hardware, software, educational theory, and practice are all used in conjunction with educational technology, also known as edutech or edtech, to facilitate learning. The sector of businesses that produce educational technology is frequently referred to by its abbreviation, edtech.EdTech companies can approach the consumers, this can be done via the schools that are convinced to use a product for free. Then, if the families want to continue to use the offering they can be charged for its usage at home. Here, schools act as lead generators for consumer adoption.They design contemporary learning spaces that enable digital immersion.They provide individualized instruction that is catered to the learning style and circumstances of each student.They offer access to a variety of information and educational opportunities without regard to location.learn more about edtech companies click here:
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If y=8 when x=4, write the direct variation equation and find y when x=5
HELPP
Answers
2=k
Y=2x
Y=2(5)
Y=10
Hence X=5, Y=10
Hudson goes to a store an buys an item that costs x dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
Answers
If Hudson having a discount coupon of 20% off, wants to buy an item having a printed price of "x" dollars, and a 5% tax is added to the discounted price in the end, then the expression that can represent the final amount Hudson paid for the item will be [(4x/5) + (x/25)].
As per the question statement, Hudson goes to a store an buy an item that costs "x" dollars, with the intention of using his 20% flat discount coupon, and then, a 5% tax is added to the final discounted price.
We are required to determine an expression that can represent the final amount Hudson paid for the item as per the above case.
Since Hudson gets a discount of 20% over the cost price of his desired item, the discounted cost price of the item becomes, [x - {(20/100) * x}]
= [x - {(1/5) * x}]
= [x - (x/5)]
= (4x/5).
And then, a 5% tax is added to the final discounted price, which takes the final amount to [(4x/5) + {(5/100) * (4x/5)]
= [(4x/5) + {(1/20) * (4x/5)]
= [(4x/5) + (x/25)]
= (21x/25)
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Evaluate 2(x - 3) if x = 15
Answers
Answer:
24
Step-by-step explanation:
2(x-3)
2(15-3)
2(12)
24
Hopes this helps please mark brainliest
Answer:
24
Step-by-step explanation:
2(x - 3)
==> plug in x = 15
2(15 - 3)
==> subtract 3 from 15
2(12)
==> multiply 2 and 12
=24
Remember we evaluate using pemdas
Parenthesis
Exponents
Multiplication and Division (going left to right)
Addition and Subtraction (going left to right)
This is the order of operations we use to determine which operation we perform. Here we first used "parenthesis" and did all operations inside of the parenthesis. We then ended with multiplication
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.
Step-by-step explanation:
Is this rat correct tell me tell me NOWWWW teehee
Answers
Answer:
No , x = -2
Step-by-step explanation:
When Dividing the Equation by a Constant , all terms in both sides must be divided by this Constant.
So here we divided both sides by 2 , but -6 is not divided , so this step is incorrect
The correct Answer is
[tex]\frac{-6}{2}+\frac{2x}{2} =\frac{-10}{2} \\-3+x=-5\\x=-5+3=-2[/tex]
Example 2 5. WALKING Lily has walked 2 miles. Her goal is to walk 6 miles. Lily plans to reach her goal by walking 3 miles each hour h for the rest of her walk. Write an equation to find the number of hours it will take Lily to reach her goal.
Answers
Answer:
y=3x-2
Step-by-step explanation:
y is for how many miles she wants to walk which is 6. she walks 3 miles per hour which is 3x (x is for hours) and -2 because she already walked 2 miles
Point A is graphed on the coordinate plane. What ordered pair represents point A?
Answers
Answer:
-7,7
Step-by-step explanation:
The solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 side touching. What is the total number of white cubes that were used to build the prism?
Answers
Answer:34?
Step-by-step explanation: not too sure but yeah
On the southeast corner of Millennium Park, there is a garden walk. It is marked off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row along which flowers will be planted.
a) If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and explain your reasoning.
b) Calculate the area of the red triangle to find the area of the garden. Show your work.
c) Millennium Park has an outdoor concert theater. Before a concert, the area reserved for special seating is roped off in the shape of a triangle as shown below. How can the converse of the Pythagorean theorem help you determine whether the roped off area is in the shape of a right triangle?
Answers
a. Using the Pythagorean Theorem, side c = 150 feet
b. Area = 5,400 ft²
c. Applying the converse of the Pythagorean Theorem, the triangle would be a right triangle if the sum of the squares of two sides equals the square of the other side.
What is the Converse of the Pythagorean Theorem?The converse of the Pythagorean theorem states that if the sum of the squares of the two smaller sides of a triangle is equal to the square of the longer side, then the triangle is a right triangle.
a. Apply the Pythagorean theorem:
c = √(a² + b²)
c = ?
a = 90 feet
b = 120 feet
Substitute
c = √(90² + 120²)
c = 150 feet
b. Area = 1/2(a)(b) = 1/2(90)(120)
Area = 1/2(10,800)
Area = 5,400 ft²
c. Using the converse of the Pythagorean Theorem, we can check if the sum of the squares of two sides equals the square of the other side.
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if he uses upper and lower control limits of 520 and 480 hours, what is the probability that a sample mean is out of control?( assuming the process standard deviation is known to be 20 hours)
Answers
0.0456 is the probability that a sample mean is out of control.
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.UCL = 520
LCL = 480
Mean (X ) = 500
Standard Deviation of sample (Sn) = 11.55
Z (for UCL) = (UCL - Mean)/Sn
Z (for UCL) = (520-500)/10
Z (for UCL) = 2
Z (for LCL) = (LCL - Mean)/Sn
Z (for LCL) = (480 - 500)/10
Z (for LCL) = -2
*Use Z table to find confidence level between Z value of -2 and 2.
Confidence level = 0.4772 + 0.4772
Confidence level = 0.9544
Risk (α ) = 1 - confidence level
Risk (α) = 1 - 0.9544
Risk (α) = 0.0456
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2. On which plane does the point (0,-1,5) lie? (1 point)
O the xy-plane
O the xz-plane
O the yz-plane
O the xyz-plane
Answers
( 0 , -1 , 5) point lies on xyz plane .
What is xyz plane ?The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.
To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.
Calculationthis given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .
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Answer both of um I'll mark you brainliest
Answers
Answer:
1) 71.83
2) 43
3) 41
4) 755.66
5) 458
6) 1757.12
7) 123 meters
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located
1,-1), and Monique's desk is located at (-4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
O√7 feet
O√14 feet
√85 feet
O√61 feet
Answers
√14 feet, A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
What is coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of numbers, or coordinates, which are written as ((x,y)).
A coordinate can be expressed in one of three ways. a coordinate with an integer for degrees, a real number for minutes, and an integer for seconds (DMS). a coordinate that contains minutes (a real number) and degrees (an integer) (MinDec). a coordinate that merely contains degrees (real number).
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A recipe calls for 6 ounces of raisins. How many milligrams of raisins is this? (1 ounce = 28.35 grams and 1 gram = 1,000 milligrams) 170.1 milligrams 1,701 milligrams 17,010 milligrams 170,100 milligrams
Answers
The measurement of a quantity requires units to be defined. The 6 ounce of raisins is equal to 171100 milligrams of it.
What is Measurement unit ?A measurement unit is unit to measure different quantities such as mass, length and time.
The measurement unit of one quantity can be converted into the other by multiplying it with a certain number.
Given that,
The amount of raisins is 6 ounces.
Since One ounce is equal to 23.85 grams,
6 ounce converted in grams equals 6 × 28.35 = 171. 10 grams
Now, 1 gram = 1000 milligrams.
Therefore, 171. 10 grams = 171.10 × 1000 milligrams
= 171100 milligrams.
Hence, 6 ounces of raisins is equivalent to 171100 milligrams.
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Answer:
A recipe calls for 170,100 milligrams of raisins.
Step-by-step explanation:
I took the exam and got it right
15. Write the factored form of 9+24 by pulling out the GCF?*
Answers
There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.
What is GCF ?In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer
. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.
CalculationGCF by listing factor method :-
Factors of 9: 1, 3, 9
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.
other two methods are attached below .
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g the center for medicare services reported that there were 295,000 reported appeals for hospitalization and other medicare part a services. for this group, 40% of the first round appeals were successful. suppose ten first round appeals were just received. the results follow a binomial distribution. what is the probability of getting more than two heads? enter answer to four decimal places.
Answers
The probability that of getting more than two heads is 0.9537.
Describe the binomial probability?There are just two options for each appeal: either it has been accepted or it wasn't. A binomial probability is employed to answer this question since the chances that one appeal will be permitted is independent of the possibility that any other appeals will be granted.The probability of precisely x successes per n repeated trials is known as a binomial probability, and X has only two possible outcomes.
P(X = x) = Cn,ₓ.pˣ(1 - p)ⁿ⁻ˣ ...eq 1
Where Cn,ₓ represents the number of distinct combinations of x items drawn from a group of n elements, as determined by the formula below.
Cn,ₓ = n!/x!(n - x)!
Where p is the likelihood that anything will happen.
10 appeals are necessary; n = 10.
Because 40% of appeals are successful; p = 0.4.
For the probability of getting at least two heads.
P(X ≥ 2) = 1 - P(X < 1)
P(X < 2) = P(X = 0) + P(X = 1)
Put the values in eq 1 and get the values for X.
P(X < 2) = 0.006 + 0.0403 = 0.0463
Now,
P(X ≥ 2) = 1 - 0.0463
P(X ≥ 2) = 0.9537
Thus, the probability that of getting more than two heads is 0.9537.
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Click the two inequalities represented by the system of inequalities graph below.
Answers
The system of inequalities that best represent the shaded feasible region shown on the graph is
y < x + 1y < -x - 2How to determine the inequalities represented inequalities graphinformation gotten from the question include
inequality graph showing shaded regions
some interpretation on the information from the question include
shading below the is less thandotted lines mean the inequality do not have equal toThis interpretation removes the first and the last options since they contain the equal to sign
positive slope moves from bottom left to top right
y < x + 1
negative slope moves from top left to down right
y < -x - 2
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Evaluate 3 (2x - 1).
Answers
Answer:
6x - 3
Step-by-step explanation:
3 ( 2x - 1 )
= 3 ( 2x ) - 3 ( 1 )
= 6x - 3
Answer:
x=1/2 or 0.5 or just 6x-3
Step-by-step explanation:
3(2x-1)
distribute.
6x-3
get 6x alone
6x=3
divide
x=3/6
x=1/2 or 0.5
Monthly charge £16
150 free minutes then 13p per minute
150 free texts then 15p per text
during one month,Jo makes 170 calls and sends 182 texts
work out the total charge for the month
Answers
The total charge for the month is £625.36.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given:
Fixed monthly plan - 616
free minutes - 150
Used minutes - 170
Free text - 150
Used text - 182
Charging amount over the free limit - 18p
Number of minutes over the limit - 170 - 150 = 20
Number of text over the limit - 182 - 150 = 32
So the extra amount that will be added to the monthly charge would be -
(20 x 0.18) +(32 x 0.18)
The total charge of the month would be -
C= 616+(20*0.18) +(32*0.18)
C= 616+3.60+5.76
C= 625.36
Therefore, the total charge for the month is £625.36.
The correct question is given below,
Here are the monthly charges for Jo's mobile phone
Monthly charge 616
150 free minutes, then 18p per minute
150 free texts, then 18p per text
During one month, Jo makes 170 minutes of calls and sends 182 texts,
Work out the total charge for the month
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In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
AB and CD are parallel lines, and PQ and PR are transversals which intersect AB at P and CD at Q and R. Angle APQ is labeled as 64 degrees, angle QPR is equal to x, angle PRD is equal to 110 degrees.
Answers
A) The value of the measure of angle x is; x = 55 degrees.
B) The way we got x is that the Internal angle between 2 parallel lines are equal and also that the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.
What is the measure of the missing angles?A) From the given image attached, we see that the angle RPB can be calculated as;
m∠RPB = 180 - 120 = 60 degrees.
This is because sum of angles on a straight line sums up to 180 degrees.
Now, by definition of alternate angles, we can say that angle BPR is equal to 60 degrees.
Thus, the value of angle x is;
x = 180 - 60 - 65
x = 55 degrees.
B) From the given diagram, we can say that;
m ∠RPB + m < PRD = 180 degrees
This is because Internal angle between 2 parallel lines are equal.
Secondly the three angles APO, x and BPR form a straight line and they sum up to 180 degrees.
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