Chapter 11.2, Problem 4GP

To determine

To find: Measures of the angles.

Answer to Problem 4GP

Angles are ${36}^0,{54}^0,{90}^0$

Explanation of Solution

Given information:

Measures of the angles of a triangle are in the ratio $2:3:5$

Given

Measures of the angles of a triangle are in the ratio $2:3:5$

Let measures of the given angles of a triangle be $2x,3x$ and $5x$

We know sum of angles of a triangle is ${180}^0$

Using that

We get

  $2x+3x+5x={180}^0$

On solving

  $\begin{array}{l}2x+3x+5x={180}^0\\ \Rightarrow 10x={180}^0\\ \Rightarrow x=\frac{{180}^0}{10}\\ \Rightarrow x^0={18}^0\end{array}$

Therefore,

  $x={18}^0$

So, angles are

One of the angle is $2x=2\left({18}^0\right)={36}^0$

Second angle is $3x=3\left({18}^0\right)={54}^0$

Third angle is $5x=5\left({18}^0\right)={90}^0$

Therefore,

Angles are ${36}^0,{54}^0,{90}^0$