Chapter 3.2, Problem 39PPS

To determine

To determine $x.$

Answer to Problem 39PPS

  $x={130}^{\circ }$

Explanation of Solution

Given information :

  

  

Let’s draw an auxiliary line.

Now it is given that $\angle 1+\angle 2=x^{\circ }$

Here in the figure we can observe that angles ${105}^{\circ }\text{and }\angle \text{1}$ are supplementary by alternate exterior angles theorem.

Similarly we can observe that angles ${125}^{\circ }\text{and }\angle 2$ are supplementary by alternate exterior angles theorem.

Hence we get,

  $\begin{array}{l}\angle 1+\angle 2=\left({180}^{\circ }-{105}^{\circ }\right)+\left({180}^{\circ }-{125}^{\circ }\right)\\ x^{\circ }={75}^{\circ }+{55}^{\circ }={130}^{\circ }\end{array}$