In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. How do you find the angle measures?

Solution:

Given, angle B is three times that of angle A.

The measure of angle C is 20 degrees more than that of angle A.

We have to find the measures of angle A, B and C.

Let the measure of angle A = x

So, measure of angle B = 3x

Measure of angle C = 20 + x

We know that the sum of the interior angles of a triangle is always equal to 180 degrees.

So, Angle A + Angle B + Angle C = 180 [angle sum property]

Substituting the values of A, B and C,

x + 3x + 20 + x = 180

5x + 20 = 180

5x = 180 - 20

5x = 160

x = 160/5

x = 32

Angle A = 32 degrees

Angle B = 3(32) = 96 degrees

Angle C = 20 + 32 = 52 degrees.

Therefore, the measures of angles are 32, 96 and 52 degrees.

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In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. How do you find the angle measures?

Summary:

In triangle ABC, the measure of angle B is three times that of angle A. The measure of angle C is 20 degrees more than that of angle A. The measures of angles are 32, 96 and 52 degrees.