An angle measures 178° more than the measure of a supplementary angle. What is the measure of each angle?

A = original angle

S = supplementary angle to angle A

By definition A+S = 180 since A and S are supplementary

Solve for S to get S = 180-A

The original angle A is 178 degrees larger than angle S, so

A = S+178

A = 180-A+178 ... replace S with 180-A

A = 358-A

A+A = 358-A+A ... adding A to both sides

2A = 358

2A/2 = 358/2 ... dividing both sides by 2

A = 179

The original angle is 179 degrees

Use this to find S

S = 180-A

S = 180-179

S = 1

The supplement to the angle A is 1 degree

Notice how the difference between

angle A = 179 degrees

angle S = 1 degree

is exactly 178 degrees (179-1 = 178)