Chapter 4.6, Problem 30PPS

To determine

The measure of angle ACD.

Answer to Problem 30PPS

  $m\angle ACD=44$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

According to the Isosceles Triangle Theorem, if the two sides of the triangle are congruent, then the angles opposite to these sides are also congruent.

Therefore,

  $\begin{array}{l}\angle CAD\cong \angle ACD;\\ m\angle CAD=m\angle ACD\end{array}$

Sum of all angles of a triangle is 180.

So,

  $\begin{array}{l}m\angle D+m\angle ACD+m\angle CAD=180\\ 92+m\angle ACD+m\angle ACD=180\\ 92+2\left(m\angle ACD\right)=180\\ 2\left(m\angle ACD\right)=180-92\\ 2\left(m\angle ACD\right)=88\\ m\angle ACD=\frac{88}{2}\\ m\angle ACD=44\end{array}$