Question

Solve the problem by multiplying first. The sum of two angles is 180°. The difference between three times the larger angle and five times the smaller angle is 252°. The system of equations braceleftze x + y = 180 3x − 5y = 252 models this situation, where x is the measure of the larger angle and y is the measure of the smaller angle. What is the measure of each angle? The measure of the larger angle is ° and the measure of the smaller angle is °.

Answer 1

36°,144°

Explanation:

x+y=180

5x+5y=900

3x-5y=252

add

8x=1152

x=144

y=180-144=36

Answer 2

The measure of the larger angle is 144° and the measure of the smaller angle is 36°.

What is the measure of each angle?

x is the measure of the larger angle

y is the measure of the smaller angle.

x + y = 180 (1)

3x − 5y = 252. (2)

From (1)

x = 180 - y

Substitute into (2)

3x − 5y = 252

3(180 - y) - 5y = 252

540 - 3y - 5y = 252

- 3y - 5y = 252 - 540

-8y = -288

Divide both sides by -8

y = -288/-8

y = 36

Therefore,

x + y = 180

x + 36 = 180

x = 180 - 36

x = 144°