Chapter 1.6, Problem 3PSA

To determine

To Prove: $m\angle VAY=2\left(m\angle RPT\right)$ .

Explanation of Solution

Given:

  

  $\angle OPT={90}^{\circ }$

Concept Used:

Bisectors divides the angle into two equal parts.

Proof:

Here, we have

  $\begin{array}{l}\angle OPT={90}^{\circ }\\ \Rightarrow \angle OPR+\angle RPT=90°\\ \Rightarrow {\left(4x\right)}^{\circ }+x^{\circ }=90°\\ \Rightarrow {\left(5x\right)}^{\circ }=90°\\ \Rightarrow x=18\\ \Rightarrow \angle RPT=x°=18°\\ \Rightarrow \angle OPR=\left(4\times 18\right)°=72°\\ \Rightarrow \angle VAY=\left(18+18\right)°=36°=2\times 18°\\ \Rightarrow m\angle VAY=2\left(m\angle RPT\right)\end{array}$