Two complementary angles. Find both angles if the measure of the first angle is 54 degrees smaller than five thirds the measure of the second angle.

Question

Suppose two angles are supplementary. Find the measures of both angles if the measure of the first angle is nine degrees smaller than eight times the measure of the second angle.

Answer 1

If angles are complementary, then their sum is 90 degrees. If one angle is x, then the other is 90 - x. So, we know:

 

x = 5/3 (90 - x) - 54

x = 150 - 5/3 x - 54

x = 96 - 5/3 x

3x = 288 - 5x

8x = 288

x = 36 degrees

 

The other angle then is 90 - 36 = 54 degrees. 

 

If angles are supplementary, their sum is 180 degrees. This time, let one angle = x and the other = 180 - x.

 

x = 8(180 - x) - 9

x = 1440 - 8x - 9

9x = 1431

x = 159 degrees, so the other angle is 180 - 159 = 21 degrees.