Question

2.

In AABC, ZB is congruent to ZC. The measure of ZB is 20 more than twice the
measure of ZA. Find the measure of each angle in AABC. [Only an algebraic
solution will be accepted.]

Answer 1

Measure of angle B: 76°

Measure of angle C: 76°

Measure of angle A: 28°

Explanation:

Equations

Let's call

x = measure of angle B

Since angle B is congruent with angle C:

x = measure of angle C

The sum of the angles in a triangle is 180°:

180 - x - x = 180 - 2x = measure of angle A

It's given the measure of angle B is 20 more than twice the measure of angle A, thus:

x = 20 + 2(180 - 2x)

Operating the parentheses:

x = 20 + 360 - 4x

Adding 4x:

5x = 380

Dividing by 5:

x = 380/5

x = 76°

Measure of angle B: 76°

Measure of angle C: 76°

Measure of angle A: 180 - 2*76°= 28°