Question

If one acute angle of the right angled triangle is half of the other, then the smallest angle is:

• A. ${90}^o$
• B. ${60}^o$
• C. ${40}^o$
• D. ${30}^o$

Answer 1

The correct option is D ${30}^o$

Let the acute angle be $x$.

Given, the acute angle is half of the other.

Then the other angle is $2x$.

We know, by angle sum property, the sum of angles of a triangle is ${180}^o$.

$⟹$ ${90}^o+2x+x={180}^o$
$⟹$ $3x={180}^o-{90}^o$
$⟹$$x=\frac{{90}^o}{3}$
$⟹$$x={30}^o$.

Hence, the angles are:

${90}^o,x={30}^o$ and $2x=2\times {30}^o={60}^o$.

Here, ${30}^o$ is the smallest angle.

Therefore, option $D$ is correct.