Question

The measures of the angles of a triangle are in the ratio $2:3:5.$Find the measures of the angles.

Answer 1

Step 1: Finding the value of x

Let the measure of the angles of a triangle be $2x,3xand5x$

We know that,

The sum of all angles in a triangle is $180°$

$$\begin{gathered} 2x+3x+5x=180 \\ \Rightarrow 10x=180 \\ \Rightarrow x=\frac{180}{10} \\ \Rightarrow x=18° \end{gathered}$$

Step 2: Finding the measure of each angle

$$\begin{gathered} 2x=2\times 18=36° \\ 3x=3\times 18=54° \\ 5x=5\times 18=90° \end{gathered}$$

Hence, the angles of a triangle are $36°,54°and90°.$