Question

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

Answer 1

Step 1: Calculate the value of ratio constant-

The angles of a triangle are in ratio = $2:3:5$

Let the ratio constant be $x$.

The angles of the triangle are = $2x,3x,5x$

By angle sum property of triangle, the sum of all the angles in a triangle is always equal to $180°$.

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

Step 2: Calculate the value of angles -

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

Hence, the angles of a triangle are $36°,54°\&90°$.