Chapter 15, Problem 3CR

To determine

To find: the value of the angle $AB$ .

Answer to Problem 3CR

  $AB={16}^{\circ }$ .

Explanation of Solution

Given:

There is concentric circle in which $CD={70}^{\circ },QR={54}^{\circ }$ .

  

Calculation:

According to the question, there is a concentric circle, where $CD={70}^{{}^0},QR={54}^{{}^0}$ .

The objective is to find $AB$ . Then,

  $\begin{array}{l}\angle APB=\frac{1}{2}QR=\frac{1}{2}\left({54}^{\circ }\right)={27}^{\circ }\\ m\angle APB=\frac{1}{2}\left(DC-AB\right)=\frac{1}{2}\left({70}^{\circ }-AB\right)\\ {27}^{\circ }={35}^{\circ }-\frac{1}{2}AB\\ \frac{1}{2}AB=8^{\circ }\\ \therefore AB={16}^{\circ }\end{array}$

Therefore, the value of the angle is $AB={16}^{\circ }$ .