Chapter 12.1, Problem 18E

To determine

To find: the measurement of the exterior angle.

Answer to Problem 18E

Exterior angle of ${68}^0$ .

Explanation of Solution

Given:

  

Concept used:

Exterior Angle theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Sum of the three angles of triangle is always ${180}^0$ .

If the triangle is right triangle then other two angles other than ${90}^0$ will be less than ${90}^0$ .

Calculation:

According to the Exterior Angle theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

According to the given:

Exterior angle $={\left(7x-16\right)}^0$ .

Two interior angles $={\left(x+8\right)}^0\text{ and }{\left(\text{4}x\right)}^0$ .

  $\begin{array}{l}{\left(7x-16\right)}^0={\left(x+8\right)}^0+{\left(4x\right)}^0.\\ 7x-16=5x+8.\\ 2x-16=8.\\ x=12.\end{array}$

Plug in the value of $x$ to find the measure of the exterior angle.

  $\begin{array}{l}{\left(7x-16\right)}^0={\left(7\left(12\right)-16\right)}^0.\\ \Rightarrow {\left(7\left(12\right)-16\right)}^0\\ {68}^0.\end{array}$

Hence, the Exterior angle of ${68}^0$ .