Chapter 11.3, Problem 2MRE

To determine

To Complete: In $\odot P$ , if the measure of the inscribed angle $RST$ is $73$ , then measure of arc $RT$ is...?

Answer to Problem 2MRE

  $146$

Explanation of Solution

Given: In $\odot P$ , if the measure of the inscribed angle $RST$ is $73$ , then measure of arc $RT$ is...

Given:

  $m\angle RPT=73$

  

  $\begin{array}{l}m\angle RPT=73\\ m\angle RPT=m\stackrel{⌢}{RT}=2m\angle RST\\ =2(73)\\ =146\end{array}$

Because the measure of the inscribed angle is half the measure of intercepted arc.

Hence,

In $\odot P$ , if the measure of the inscribed angle $RST$ is $73$ , then measure of arc $RT$ is $146$ .