Chapter 8.6, Problem 35E

To determine

Solution of an algebraic equation based on the given description.

Answer to Problem 35E

The measure of one angle is $63°$ .

The measure of second angle is $180°-63°=117°$ .

Explanation of Solution

Given:

Two angles form a linear pair. The measure of one is 15 degrees less than 2/3 the measure of the other.

Calculation:

Let the measure of the angle of the linear pair be x degrees.

The measure of the other angle will be 180 − x degrees.

The solution to given problem will be:

  $\begin{array}{l}x°=\frac{2}{3}\left(180°-x°\right)-15°\\ x=\frac{2}{3}\left(180-x\right)-15\\ x=\frac{2\left(180-x\right)-45}{3}\\ 3x=360-2x-45\\ 3x+2x=360-45\\ 5x=315\\ x=\frac{315}{5}\\ x=63°\end{array}$

The measure of one angle is $63°$ .

The measure of second angle is $180°-63°=117°$ .