Chapter 8.6, Problem 49E

(a)

To determine

To find: The expression for measurement of $\angle BAE,\angle DAE$ and $\angle CAB$ .

Answer to Problem 49E

The required expressions are:

  $\begin{array}{l}\Rightarrow \angle BAE=y\\ \Rightarrow \angle DAE=180°-y\\ \Rightarrow \angle CAB=180°-y\end{array}$

Explanation of Solution

Given information: The following diagram is been given.

  

Calculation: The expression for the measurement of $\angle BAE,\angle DAE$ and $\angle CAB$ will be as follows:

From the given diagram,

Vertical angles: $\angle BAE=y$

Supplementary angles: $\angle DAE=180°-y$ and $\angle CAB=180°-y$

(b)

To determine

To explain: The thing you noticed about the measures of vertical angles.

Explanation of Solution

Given information: The following diagram is been given.

  

The vertical angles are equal in measures because $\angle y$ has $180°-y$ for each, whichever you measure.