Chapter 11.4, Problem 1CYU

To determine

To find the missing angles in the given quadrilateral.

Answer to Problem 1CYU

$x={57}^{\circ }$ & missing angles are ${114}^{\circ }\&{57}^{\circ }$ .

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

  $\begin{array}{l}2x^{\circ }+x^{\circ }+{124}^{\circ }+{65}^{\circ }={360}^{\circ }\\ \Rightarrow 3x^{\circ }+{189}^{\circ }={360}^{\circ }\\ \Rightarrow 3x^{\circ }={360}^{\circ }-{189}^{\circ }\\ \Rightarrow 3x^{\circ }={171}^{\circ }\\ \Rightarrow x^{\circ }={57}^{\circ }\end{array}$

Therefore missing angles are,

  $\begin{array}{l}2x=2\times {57}^{\circ }={114}^{\circ }\\ \&x={57}^{\circ }\end{array}$