Question

If two complementary angles are in the ratio 3: 2, then what is the measure of the bigger angle?

• A. ${90}^{\circ }$
• B. ${54}^{\circ }$
• C. ${18}^{\circ }$
• D. ${36}^{\circ }$

Answer 1

The correct option is B ${54}^{\circ }$

Given, two complementary angles are in the ratio 3:2.

Let the angles be 3x and 2x.

Since, the sum of two complementary angles is a right angle.
$3x+2x={90}^{\circ }$

$\Rightarrow 5x={90}^{\circ }$

$\Rightarrow x={18}^{\circ }$

Measure of the bigger angle
= $3\times {18}^{\circ }$
$={54}^{\circ }$