Chapter 11.1, Problem 14IP

a.

To determine

To find: The relationship between $\angle 1$ and $\angle 2$

Answer to Problem 14IP

Relationship between $\angle 1$ and $\angle 2$ is

  $\angle 1+\angle 2={90}^0$

Explanation of Solution

Given information:

Semicircular window

From the given figure

We can say that $\angle 1$ and $\angle 2$ forms a right angle; it means they are complementary angles.

So, the sum of their measures is ${90}^0$ .

  $\angle 1+\angle 2={90}^0$

Therefore,

Relationship between $\angle 1$ and $\angle 2$ is

  $\angle 1+\angle 2={90}^0$

b.

To determine

To find: $m\angle 1$

Answer to Problem 14IP

  $\angle 1={66}^0$

Explanation of Solution

Given information:

Semicircular window

  $m\angle 2={24}^0$

From the given figure

We can say that $\angle 1$ and $\angle 2$ forms a right angle; it means they are complementary angles.

So, the sum of their measures is ${90}^0$ .

  $\begin{array}{l}\angle 1+\angle 2={90}^0\\ \Rightarrow \angle 1+{24}^0={90}^0\\ \Rightarrow \angle 1={90}^0-{24}^0\\ \Rightarrow \angle 1={66}^0\end{array}$

Therefore,

  $\angle 1={66}^0$