Chapter 7.1, Problem 15PSB

To determine

To calculate : The measure of the exterior angle at the third vertex.

Answer to Problem 15PSB

The measure of the exterior angle at the third vertex is ${110}^0$

Explanation of Solution

Given information : The following information has been given for $\Delta ABC$

  $\angle A:\angle B=2:3$

  $\angle C=4^0+\angle B$

Formula used : Sum of the angles of any triangle add up to ${180}^0$

Calculation : Let us assume $\angle A=2x$ and $\angle B=3x$ , and $\angle C=4^0+3x$ .

Now, we know that the sum of the angles of any triangle add up to ${180}^0$ . Thus, we add up the angles. We get

  $2x+3x+4^0+3x={180}^0\to x={22}^0$

Now, we know that $\angle C=4^0+3x$ . Thus, we get

  $\angle C={70}^0$

The measure of the exterior angle at the third vertex is

  ${180}^0-\angle C={110}^0$