Chapter 1.2, Problem 16PSB

To determine

To find : The value of $m\angle POC$ .

Answer to Problem 16PSB

  $m\left(\angle POC\right)=66°9^{\prime }$

Explanation of Solution

Given information :

  

  $\begin{array}{l}m\angle POA=90°\\ m\left(\angle POC\right)=3m\left(\angle COA\right)\end{array}$

Concept used : Measure of right angle is $90°$

  $1°=6^{\prime }$

Calculation:

Here, we have

  $\begin{array}{l}m\angle POA=90°\\ m\left(\angle POC\right)=3m\left(\angle COA\right)\\ \because \angle POC+\angle COA=\angle POA\\ \Rightarrow 3\angle COA+\angle COA=90°\\ \Rightarrow 4\angle COA=90°\\ \Rightarrow \angle COA=22.5°\\ \Rightarrow \angle COA=22°+0.5°\\ \Rightarrow \angle COA=22°+0.5\times 6^{\prime }\\ \Rightarrow \angle COA=22°+3^{\prime }\\ \Rightarrow \angle COA=22°3^{\prime }\\ \because m\left(\angle POC\right)=3m\left(\angle COA\right)\\ \Rightarrow m\left(\angle POC\right)=3\times 22°3^{\prime }=66°9^{\prime }\end{array}$

Conclusion:

  $m\left(\angle POC\right)=66°9^{\prime }$