Chapter 12.1, Problem 16E

To determine

To find: the measurement of the exterior angle.

Answer to Problem 16E

Exterior angle is ${92}^0$ .

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 $={\left(2x-2\right)}^0$ .

Two interior angles $=x^0{\text{ and 45}}^0$ .

  $\begin{array}{l}{\left(2x-2\right)}^0=x^0+{45}^0.\\ 2x-2=x+45.\\ x-2=45.\\ x=47.\end{array}$

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

  $\begin{array}{l}{\left(2x-2\right)}^0={\left(2\left(47\right)-2\right)}^0.\\ \Rightarrow {\left(2\left(47\right)-2\right)}^0\\ {92}^0.\end{array}$

Hence, the Exterior angle of ${92}^0$ .