Chapter 5.3, Problem 13PSA

To determine

To Find: The value of $x\text{and }m\angle 1$ .

Answer to Problem 13PSA

  $m\angle 1=\text{42}{\text{.2008}}^{\circ }$

Explanation of Solution

Given:

  

Concept Used:

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

Calculation:

Here, we have

  $\begin{array}{l}{\left(2.14x\right)}^{\circ }={\left(x+22.4808\right)}^{\circ }\left(\text{Alternate interior angles}\right)\\ \Rightarrow 1.14x=22.4808\\ \Rightarrow x=\frac{22.4808}{1.14}=19.72\\ \because m\angle 1={\left(2.14x\right)}^{\circ }\\ \Rightarrow m\angle 1={\left(2.14\times 19.72\right)}^{\circ }=\text{42}{\text{.2008}}^{\circ }\\ \therefore m\angle 1=\text{42}{\text{.2008}}^{\circ }\end{array}$