Question

The acute angles of a right triangle are in the ratio $4:5$ . Find the measure of these angles .

Answer 1

In right angled triangle , one angle is 90° so the sum of two acute angles will be 90° due to the angle sum property of the triangle .

Now ratio of acute angles is $4:5$ , Lets assume the angles be $4x$ and $5x$

$$\begin{gathered} \Rightarrow 4x+5x=90° \\ \Rightarrow 9x=90° \\ \Rightarrow x=\frac{90°}{9} \\ \Rightarrow x=10° \end{gathered}$$

substituting the value of $x$ in the angles result in

$$\begin{gathered} 4x=4\times 10°=40° \\ 5x=5\times 10°=50° \end{gathered}$$

Therefore the angles of the triangle are 40° , 50° and 90° .