Question

If the difference of two complementary angles is ${30}^{\circ }$, then find the angles.

• A. 30 degrees and 60 degrees
• B. 35 degrees and 60 degrees
• C. 25 degrees and 55 degrees
• D. 20 degrees and 70 degrees

Answer 1

The correct option is A 30 degrees and 60 degrees

When the sum of two angles is ${90}^{\circ }$, then the angles are called complementary angles.

Let one of the angles measure $x^{\circ }$.
So, the measure of the other angle $=(90-x{)}^{\circ }$

Given, the difference of the two complementary angles is ${30}^{\circ }$.

So, $(90-x)-x={30}^{\circ }$
$\Rightarrow 2x={60}^{\circ }$
$\Rightarrow x={30}^{\circ }$

Henve , the angles are ${30}^{\circ }$ and $(90-30)={60}^{\circ }$