Question

If two complementary angles are in the ratio 3 :2, then find the measure of the greater angle.

• A. ${54}^o$
• B. ${55}^o$
• C. ${36}^o$
• D. ${42}^o$

Answer 1

The correct option is A ${54}^o$

Given , the angles are in the ratio 3:2.
Let the angles be 3x and 2x.

We know that the sum of two complementary angles is 90 degrees.

$\therefore$ 3x + 2x = ${90}^o$

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

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

So, the measure of the greater angle
$=3\times 18={54}^o$