Question

The difference of the measures of two supplementary angles is 30°. find the measure of each angle.

Answer 1

Supplementary angles are angles which have a sum equal to 180 degrees. Let us say that the angles are x and y therefore:

x + y = 180

 

Assuming that x is the larger angle, so the difference is:

x – y = 30

 

Combining the two equations:

x + y + x – y = 180 + 30

2 x = 210

x = 105 degrees

 

 y = 75 degrees

 

The two angles are 105° and 75°