Chapter 2.5, Problem 13PSB

To determine

To Prove : $\angle NPS\cong \angle WEX$

Answer to Problem 13PSB

  $\angle NPS\cong \angle WEX$

Explanation of Solution

Given information:

  $\begin{array}{l}\angle NPR={90}^{\circ }\\ \overline{WE}\perp \overline{ET}\\ \angle SPR\cong \angle XET\end{array}$

  

  $\begin{array}{l}\because \angle NPR={90}^{\circ }\\ \angle NPS+\angle NPS={90}^{\circ }\mathrm{....}(1)\\ \because \overline{WE}\perp \overline{ET}\\ \therefore \angle WET={90}^{\circ }\\ \therefore \angle WEX+\angle XET={90}^{\circ }\mathrm{....}(2)\\ from\_eq.(1)\&(2)\\ \angle NPS+\angle \bcancel{R}PS=\angle WFX+\angle \bcancel{X}ET\\ \angle NPS\cong \angle WEX\end{array}$