The measure of the largest scale of a triangle is 40o more than the measure of the smallest angle, and the measure of the remaining angle is 20o more than the measure of the smallest angle. Find the measure of each angle.
Answer:
40°, 60°, 80°
Step-by-step explanation:
You want the measures of the three angles of a triangle if the larger angles are 20° and 40° greater than the smallest.
Middle angleThe largest angle is 20° more than the middle angle, and the smallest is 20° less. Then the sum of the three angles is 3 times the middle angle, which must be 180°/3 = 60°.
The three angles are 40°, 60°, 80°.
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Additional comment
If you need equations, you can designate the angles a, b, c, smallest to largest. Then c=a+40, and b=a+20. The sum is ...
(a) +(a +20) +(a +40) = 3a +60 = 180
Dividing by 3 tells you ...
a +20 = 60 . . . . . matches the value of b
a = 60 -20 = 40
c = 40 +40 = 80
If we were to write the equations in terms of b, we would have ...
(b -20) +b +(b +20) = 180
3b = 180
b = 60
This version gives a 1-step equation to solve instead of a 2-step equation, easier to do mentally.
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The measure of the Angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.
The measure of the smallest angle as x.
According to the given information, the largest angle is 40 degrees more than the smallest angle. Therefore, the measure of the largest angle is x + 40.
Similarly, the remaining angle is 20 degrees more than the smallest angle. So, the measure of the remaining angle is x + 20.
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
x + (x + 40) + (x + 20) = 180.
Simplifying the equation, we have:
3x + 60 = 180.
Subtracting 60 from both sides of the equation:
3x = 120.
Dividing both sides by 3:
x = 40.
Therefore, the measure of the smallest angle is 40 degrees.
Using this value, we can find the measures of the other two angles:
The largest angle is x + 40 = 40 + 40 = 80 degrees.
The remaining angle is x + 20 = 40 + 20 = 60 degrees.
the measure of the angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.
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