Chapter 9.3, Problem 9PSA

To determine

To find: The values of following angles i.e. $m\angle HJP,m\angle HKP\text{ and }m\angle HMP$ .

Answer to Problem 9PSA

The Values of all three unknown angles are $25°$ .

Explanation of Solution

Given information :

  $\angle HOM\text{}=50°$

Formula used :

The angle is formed by radius of a circle, is twice of the angle, which is formed by the chords on its perimeter.

Calculation :

Since, $m\angle HJP,m\angle HKP\text{ and }m\angle HMP$ are formed by the chords of the circle. So, the value of each angle is half of the angle formed at the center. i.e., $\angle HOM\text{}=50°$

  $\begin{array}{l}m\angle HJP\text{=}\frac{\angle HOM}{2}=\frac{{50}^{\text{o}}}{2}={25}^{\text{o}}\\ \text{Similarly},m\angle HMP=m\angle HKP\text{=}\frac{\angle HOM}{2}=\frac{{50}^{\text{o}}}{2}={25}^{\text{o}}\\ \therefore m\angle HJP\text{= }m\angle HKP=m\angle HMP\text{ =25}°\end{array}$