Chapter E, Problem 9.9EX

To determine

To find: The measure of $\angle X$ .

Answer to Problem 9.9EX

The measure of $\angle X=35$ .

Explanation of Solution

Given information: If $m\stackrel{⌢}{BC}=120$ and $m\stackrel{⌢}{AD}=50$

Calculation: If $m\stackrel{⌢}{BC}=120$ and $m\stackrel{⌢}{AD}=50$

  $\begin{array}{l}\text{If }m\stackrel{⌢}{BC}=120\\ \text{Then }\angle BAC=\angle BDC=60\\ \text{If }m\stackrel{⌢}{AD}=50\\ \text{Then }\angle ABD=\angle ACD=25\\ \angle BAC+\angle ABD+\angle BYA=180\\ \text{Given }\angle BAC=60,\angle ABD=25\\ \text{Then }\angle BYA=95\\ \text{And }\angle AYD=85\\ \angle XAY=\angle XDY=120\\ \text{Then }\angle AXD+\angle XAY+\angle XDY+\angle AYD=360\\ \text{Given }\angle XAY=\angle XDY=120,\angle AYD=85\\ \angle AXD+120+120+85=360\\ \angle AXD=35\end{array}$