Chapter 12, Problem 15MCQ

To determine

To find: The measure of the $\angle {\text{w}}^{\circ }$ .

Answer to Problem 15MCQ

The measure of the unknown angle $\angle {\text{w}}^{\circ }$ is ${94}^{\circ }$ .

Explanation of Solution

Given information:

  

Calculation:

The given figure is a pentagon which is a five sided polygon.

The sum of the interior angles of a polygon $=(\text{n}-2)\times {180}^{\circ }$

Where, for the pentagon $\text{n}=5$

The sum of the interior angles of the pentagon is,

  $\begin{array}{l}=(\text{n}-2)\times {180}^{\circ }\\ =(5-2)\times {180}^{\circ }\\ =3\times {180}^{\circ }\\ ={540}^{\circ }\end{array}$

Therefore, $\text{w}+{134}^{\circ }+{120}^{\circ }+{109}^{\circ }+{83}^{\circ }={540}^{\circ }$$\mathrm{......}(1)$

Let’s find the value of the unknown angle from the equation $(1)$ ,

  $\begin{array}{c}\text{w}+{134}^{\circ }+{120}^{\circ }+{109}^{\circ }+{83}^{\circ }={540}^{\circ }\\ \text{w}+{446}^{\circ }={540}^{\circ }\\ \text{w}={540}^{\circ }-{446}^{\circ }\\ \text{w}={94}^{\circ }\end{array}$

Hence, The measure of the unknown angle $\angle {\text{w}}^{\circ }$ is ${94}^{\circ }$ .