Chapter 7.3, Problem 2PSA

Solution

To Calculate: The measure of the $\angle E$

The required measure of $\angle E$ is ${40}^{\circ }$

Given information: $m\angle A=160$ , $m\angle B=50$ , $m\angle C=140$ and $m\angle D=150$ is provided in the question which will help to find the solution.

Formula used: Here, we are using the formula

Sum of angles is = $(n-2)\times {180}^{\circ }$

Calculation: So that, sum of angles = $(n-2)\times {180}^{\circ }$

➔ $(5-2)-{180}^{\circ }$

➔ ${540}^{\circ }$

Now, According to question

$m\angle A+m\angle B+m\angle C+m\angle D+m\angle E={540}^{\circ }$

➔ ${160}^{\circ }+{50}^{\circ }+{140}^{\circ }+{150}^{\circ }+m\angle E={540}^{\circ }$

➔ $m\angle E={40}^{\circ }$

Hence, the required measure is $m\angle E={40}^{\circ }$