Question

If two acute angles of a right angles triangle are in the ratio $2:3$, find the measure of all angles of the triangle.

Answer 1

Step 1 : In the question it is mentioned that it is a right angled triangle, so one angle of the triangle is of $90°$

Step 2 : Lets take a multiplier $x$ to get the other two angles of the triangle, so the other two angles are $2xand3x$

Step 3 : Now apply the angle sum property of the triangle.

$$\begin{gathered} 2x+3x+90°=180° \\ 5x+90°=180° \\ 5x=180°-90° \\ 5x=90° \\ x=\frac{90°}{5} \\ x=18° \end{gathered}$$

Step 4 : Put the value of $x$ to get the value of other two angles of the triangle.

First angle $2x=2\left(18\right)=36°$

Second angle $3x=3\left(18\right)=54°$

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