Chapter 11, Problem 14CUR

To determine

To Find:

1. Numerical Value of each angle of the triangle.
2. To find the type of triangle.

Answer to Problem 14CUR

1. $m\angle R=50°,m\angle S=50°,m\angle T=80°$
2. It is an isosceles triangle because two angles are equal to each other.

Explanation of Solution

Given:

The angles of a triangle $\Delta RST$ are:

  $m\angle R=2x+10,m\angle S=3x-10,m\angle T=4x$

The sum of all the interior angles of a triangle is equal to $180°$ .

  $\begin{array}{l}m\angle R+m\angle S+m\angle T=180°\\ \Rightarrow 2x+10+3x-10+4x=180°\\ \Rightarrow 9x=180°\\ \Rightarrow x=20°\end{array}$

Measure of each angle is:

  $m\angle R=50°,m\angle S=50°,m\angle T=80°$

It is an isosceles triangle because two angles are equal to each other.