Chapter E, Problem 9.10EX

To determine

To find: the measures of $\angle 1$ .

Answer to Problem 9.10EX

the measures of $\angle 1=95$ .

Explanation of Solution

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

Calculation:

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

  $\begin{array}{l}\text{If }m\stackrel{⌢}{BC}=120\\ \text{Then }\angle BAC=\angle BDC=60\\ \text{If }m\stackrel{⌢}{AD}=50\\ \text{Then }\angle ABD=\angle ACD=25\\ \angle BAC+\angle ABD+\angle BYA=180\\ \text{Given }\angle BAC=60,\angle ABD=25\\ \text{Then }\angle BYA=95\\ \angle AYB=\angle BYA=95\end{array}$