Question

In a right triangle, one of the acute angles is $9^{\circ }$ less than twice the other acute angle.

Find the measure of each acute angle.

Answer 1

Explanation:

In a triangle ,all internal angles sum up to $180°$.

Given, right angled triangle,

$\Rightarrow oneangle=90°$

Let the acute angle be $x$

then the other acute angle will be $2x-9°$

Using internal angle sum,

$\begin{array}{rcl}& \Rightarrow & 90+x+2x-9=180°\\ & \Rightarrow & 3x=99°\\ & \Rightarrow & x=33°\\ & & \end{array}$

Therefore , the acute angles are $33°$ and $57°$.