Question

In a right angled triangle, the difference between two acute angles is $\frac{\pi }{9}$ in circular measure. Express the angles in degrees.

• A. $30^{\circ }$, $60^{\circ }$
• B. $55^{\circ }$, $35^{\circ }$
• C. $50^{\circ }$, $30^{\circ }$
• D. $40^{\circ }$, $50^{\circ }$

Answer 1

Answer: (B)

Since the triangle is right angled, therefore, the sum of the two acute angles is $90^{\circ }$. $(\because$ third angle $=90^{\circ })$
Let the two acute angles be $x$ and $y$, $x>y$
then $x+y=90^{\circ }\dots (i)$
Also, $x-y=\frac{\pi }{9}$ radian (given)
$\Rightarrow x-y=20^{\circ }\dots \left(ii\right)$
Adding $\left(i\right)$ and $\left(ii\right)$, we get $2x=110^{\circ }$
$\Rightarrow x=55^{\circ }$,
Putting it in $\left(i\right)$, we get $55^{\circ }+y=90^{\circ }$
$\Rightarrow y=35^{\circ }$,
Hence, the two acute angles are $55^{\circ },35^{\circ }$.