Chapter 12.3, Problem 18E

To determine

To find :themeasure ofan exterior angle at vertex A ,vertex B, vertex C.

Answer to Problem 18E

The measure of an exterior angle at vertex A is ${148}^{\circ }$

At vertex B is ${79}^{\circ }$

At vertex C is ${133}^{\circ }$ .

Explanation of Solution

Given : from the triangleprovided in the question, it is observed that

  $\begin{array}{l}\angle A={32}^{\circ }\\ \angle B={101}^{\circ }\\ \angle C={47}^{\circ }\end{array}$

Formula used: the measure of an exterior angle at vertex = ${180}^{\circ }$ -interior angle at that vertex.

Calculation: let x be the exterior angle at vertex A,

So exterior angle at vertex A

  $\begin{array}{l}x={180}^{\circ }-{32}^{\circ }\\ x={148}^{\circ }\end{array}$[subtract]

Let y be the exterior angle at vertex B,

  $\begin{array}{l}y={180}^{\circ }-{101}^{\circ }\\ y={79}^{\circ }\text{ [subtract]}\end{array}$

Let z be the exterior angle at vertex C,

  $\begin{array}{l}z={180}^{\circ }-{47}^{\circ }\\ z={133}^{\circ }\text{ [subtract]}\end{array}$

Hence,The measure of an exterior angle at vertex A is ${148}^{\circ }$

At vertex B is ${79}^{\circ }$

At vertex C is ${133}^{\circ }$ .