Chapter 11.4, Problem 31STP

To determine

To find the value of x by using the given figure.

Answer to Problem 31STP

  $x={50}^{\circ }$

Explanation of Solution

Given:

Concept used:

The sum of all the interior angles of a quadrilateral is ${360}^{\circ }$ .

Calculation:

Since the sum of all the interior angles of a quadrilateral is ${360}^{\circ }$ , therefore we get

  $\begin{array}{l}{x}^{\circ }+{130}^{\circ }+x^{\circ }+{130}^{\circ }={360}^{\circ }\\ \Rightarrow 2x^{\circ }+{260}^{\circ }={360}^{\circ }\\ \Rightarrow 2x^{\circ }={360}^{\circ }-{260}^{\circ }\\ \Rightarrow 2x^{\circ }={100}^{\circ }\\ \Rightarrow x^{\circ }={50}^{\circ }\end{array}$