Chapter 12.1, Problem 24E

a.

To determine

To find:The angle $m\angle 1$

Answer to Problem 24E

The measure of the angle $m\angle 1={75}^{\circ }$ .

Explanation of Solution

Given:

  $\angle 1$ and ${15}^{\circ }$ are complementary angles.

Calculation:

Since,

Complementary angles measure ${90}^{\circ }$ .

Therefore,

  $m\angle 1+{15}^{\circ }={90}^{\circ }$

  $\begin{array}{l}\Rightarrow m\angle 1={90}^{\circ }-{15}^{\circ }\\ \Rightarrow m\angle 1={75}^{\circ }\end{array}$

Hence, the measure of the angle $m\angle 1={75}^{\circ }$ .

b.

To determine

To find: The angle $m\angle 2$ .

Answer to Problem 24E

The measure of the angle $m\angle 2={105}^{\circ }$ .

Explanation of Solution

Given:

The angle measure $m\angle 1={75}^{\circ }$ .

Calculation:

Since, linear angles measures ${180}^{\circ }$ .

Therefore,

  $\angle 1$ and $\angle 2$ are supplementary angles.

  $\Rightarrow m\angle 1+m\angle 2={180}^{\circ }$

Since,

  $m\angle 1={75}^{\circ }$

  $\begin{array}{l}\Rightarrow {75}^{\circ }+m\angle 2={180}^{\circ }\\ \Rightarrow m\angle 2={180}^{\circ }-{75}^{\circ }\\ \Rightarrow m\angle 2={105}^{\circ }\end{array}$

Hence, the measure of the angle $m\angle 2={105}^{\circ }$ .