Chapter 11.4, Problem 30STP

To determine

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

Answer to Problem 30STP

  $x^{\circ }={95}^{\circ }$ & option C is correct.

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

  $\begin{array}{l}{90}^{\circ }+{75}^{\circ }+x^{\circ }+{100}^{\circ }={360}^{\circ }\\ \Rightarrow x^{\circ }+{265}^{\circ }={360}^{\circ }\\ \Rightarrow x^{\circ }={360}^{\circ }-{265}^{\circ }\\ \Rightarrow x^{\circ }={95}^{\circ }\end{array}$

Hence option C is correct.