Chapter 10, Problem 2RP

To determine

To find : The value of x and y

Answer to Problem 2RP

  $x=66°$ and $y=32°$

Explanation of Solution

Given information :

We know that, $\stackrel{⌢}{AB}=98°$ and $\stackrel{⌢}{CD}=34°$ .

  

Formula Used:

The angle subtended by an arc of a circle as its centre is twice of a angle it subtends anywhere on the circle's circumference.

Calculation :

  $\begin{array}{l}\angle \text{ADB}=\angle \text{ACB}=\frac{1}{2}\times 98°=49°\\ \angle \text{CAD}=\angle \text{CBD}=\frac{1}{2}\times 34°=17°\end{array}$

Now $x=49°+17°=66°$

Now,

  $\begin{array}{l}\angle \text{PCT}+\angle \text{TDP}+\angle \text{DPC}+y=360°\\ \Rightarrow y=360°-328°\\ \Rightarrow y=32°\end{array}$

Hence, $\angle x=66°$ and $\angle y=32°$