Chapter 5.3, Problem 8PSA

To determine

To Find: The value of $m\angle X\text{and }m\angle W.$ .

Answer to Problem 8PSA

  $m\angle X={70}^{\circ }\text{and }m\angle W={110}^{\circ }$

Explanation of Solution

Given:

  

  $\begin{array}{l}\overline{ST}\parallel \overline{XW}\\ \overrightarrow{ST}\text{bisects }\angle VSW\end{array}$

Concept Used:

Exterior angle is equal to the sum of two interior opposite angles.

  $\begin{array}{l}\text{Sum of interior angles of triangle }={180}^{\circ }\\ \text{Also, sum of linear pair of angles }={180}^{\circ }\end{array}$

Calculation:

  $\begin{array}{l}\text{Since, sum of linear pair of angles }={180}^{\circ }\\ \Rightarrow \angle VSW+\angle XSW={180}^{\circ }\\ \Rightarrow \angle VSW+{40}^{\circ }={180}^{\circ }\\ \Rightarrow \angle VSW={140}^{\circ }\\ \Rightarrow \angle VST={70}^{\circ }\left(\because \overrightarrow{ST}\text{bisects }\angle VSW\right)\\ \Rightarrow \angle SXW={70}^{\circ }\left(\because \overline{ST}\parallel \overline{XW}\right)\\ \Rightarrow m\angle X={70}^{\circ }\\ \text{Since, sum of interior angles of triangle}={180}^{\circ }\\ \Rightarrow \angle SWX+\angle WXS+\angle WSX={180}^{\circ }\\ \Rightarrow \angle SWX+{70}^{\circ }+{40}^{\circ }+={180}^{\circ }\\ \Rightarrow \angle SWX={110}^{\circ }\\ \Rightarrow m\angle W={110}^{\circ }\end{array}$