Chapter 11, Problem 21CCSR

To determine

Find the measure in degrees of the one of the other two angles.

Answer to Problem 21CCSR

The measure of the one of the other two angles is ${30}^0$

Explanation of Solution

Given:

A roof on a house has triangular cross section with at least two angles of equal measure. One angle of the triangle measures 120 deg. What is the measure, in degrees of one of the other two angles?

Concept Used:

The sum of the interior angles of a Triangle is ${180}^0$ .

Calculation:

The sum of the interior angles of a Triangle is ${180}^0$ .

Let x be the measure of the angle with equal measure so that the sum is: ${120}^0+x+x={180}^0$

Solve for x:

  $\begin{array}{l}{120}^0+x+x={180}^0\\ {120}^0-{120}^0+2x={180}^0-{120}^0\\ 2x={60}^0\\ \frac{2x}{2}=\frac{{60}^0}{2}\\ x={30}^0\end{array}$

The measures of the other two angles are ${30}^0$ each.

Thus, the measure of the one of the other two angles is ${30}^0$