Solve the problem.
-Angle A and angle B are supplementary angles and angle A is 15° less than four times angle B. Find the measures of angle A and angle B.
A) A = 147°, B = 33°
B) A = 125°, B = 55°
C) A = 141°, B = 39°
D) A = 156°, B = 24°

Question

Solve the problem.
-Angle A and angle B are supplementary angles and angle A is 15° less than four times angle B. Find the measures of angle A and angle B. 
A) A = 147°, B = 33° 
B) A = 125°, B = 55° 
C) A = 141°, B = 39° 
D) A = 156°, B = 24°

Quizplus · Accepted Answer

Let x be the measure of angle B.

Angle A is 15 less than four times angle B, so:
A = 4x - 15

Angle A and angle B are supplementary, so:
A + B = 180

Substitute A with 4x-15: 
4x-15 + x = 180

Simplify and solve for x:
5x - 15 = 180 
5x = 195 
x = 39

Therefore, 
A = 4x - 15 = 141

The measures of angle A and angle B are 141° and 39° respectively, which matches the answer choice C. Let x be the measure of angle B.
Since angle A is 15° less than four times angle B, we have:
A = 4x - 15
Since angle A and angle B are supplementary, their sum is 180°. Therefore:
A + B = 180
Substituting A = 4x - 15, we get:
4x - 15 + x = 180
Simplifying this equation, we get:
5x = 195
x = 39
Substituting x = 39 back into A = 4x - 15, we get:
A = 141
Therefore, the measures of angle A and angle B are 141° and 39° respectively, and the answer is choice C.

Solve the Problem. -Angle a and Angle B Are Supplementary Angles and Angle