Chapter 11.4, Problem 7PPS

To determine

To find the missing angles in the given quadrilateral.

Answer to Problem 7PPS

$x={22}^{\circ }$ & missing angle is ${44}^{\circ }$ .

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

  $\begin{array}{l}\Rightarrow {94}^{\circ }+{107}^{\circ }+2x^{\circ }+{115}^{\circ }={360}^{\circ }\\ \Rightarrow 2x^{\circ }+{316}^{\circ }={360}^{\circ }\\ \Rightarrow 2x^{\circ }={360}^{\circ }-{316}^{\circ }\\ \Rightarrow 2x^{\circ }={44}^{\circ }\\ \Rightarrow x^{\circ }={22}^{\circ }\end{array}$

Therefore missing angle is,

  $2x^{\circ }=2\times {22}^{\circ }={44}^{\circ }$