Chapter 12.1, Problem 33E

n

To determine

To find:Themeasure of the angles,

  $\angle 1,\angle 2$ when they are complementary angles and when they are supplementary angles.

Answer to Problem 33E

When two of the angles are complementary, they measure ${45}^{\circ }$ each and when two of the angles are supplementary, they measure ${90}^{\circ }$ each.

Explanation of Solution

Given information: Two angles

  $\angle 1,\angle 2$ .

Since, complementary angles are those whose sum of the angles is ${90}^{\circ }$ . That is $m\angle 1+m\angle 2={90}^{\circ }$ .

Therefore,when two of the angles are complementary, they will measure ${45}^{\circ }$ each.

Since, supplementary angles are those whose sum of the angles is ${180}^{\circ }$ . That is $m\angle 1+m\angle 2={180}^{\circ }$ .

When two angles are supplementary, they will measure ${90}^{\circ }$ each.

Thus, when two of the angles are complementary, they measure ${45}^{\circ }$ each and two angles are supplementary, they measure ${90}^{\circ }$ each.