Chapter 5.3, Problem 10PSA

To determine

To Find: The value of $m\angle 8$ .

Answer to Problem 10PSA

  $m\angle 8={150}^{\circ }$

Explanation of Solution

Given:

  

  $f\parallel g$

Concept Used:

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

  $\text{Sum of interior angles of triangle }={180}^{\circ }$

Calculation:

Now we draw a line h parallel to lines f and g, such as

  

Since, $f\parallel g$

  $\begin{array}{l}\Rightarrow \angle 1={70}^{\circ }\\ \Rightarrow \angle 2={80}^{\circ }\\ ++\angle KLM+\angle LMK={180}^{\circ }\\ \Rightarrow \angle 8=\angle 1+\angle 2={70}^{\circ }+{80}^{\circ }={150}^{\circ }\\ \therefore m\angle 8={150}^{\circ }\end{array}$