Chapter 5.3, Problem 5PSA

To determine

To Find: The value of $m\angle 1.$ .

Answer to Problem 5PSA

  $m\angle 1={41}^{\circ }$

Explanation of Solution

Given:

  

  $a\parallel b$

Concept Used:

When two parallel lines are intersected by a transversal corresponding angles are equal.

Calculation:

  $\begin{array}{l}\text{Since, when two parallel lines are intersected by a transversal corresponding angles are equal}\text{.}\\ \Rightarrow \left(2x+5\right)°=\left(3x-13\right)°\\ \Rightarrow x=18\\ \Rightarrow m\angle 1=\left(2\times 18+5\right)°={41}^{\circ }\\ \therefore m\angle 1={41}^{\circ }\end{array}$