Question

An angle measures 30° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Hi there!

`\boxed{\angle A = 75^o, \angle B = 105^o}`

Let there be two angles, ∠A and ∠B, that are supplementary to each other. Therefore:

∠A + ∠B = 180°

We can assign ∠B to be the greater angle. Assume ∠A has a measure of x°.

∠A = x°

∠B = x° + 30°

The sum is equal to 180°, so:

x° + (x° + 30°) = 180°

Solve for x°.

2x° + 30° = 180°

2x° = 150°

x° = 75°

Thus, ∠A = 75°.

Since ∠B is 30°, greater:
∠B = 75° + 30° = 105°.