Question

Two supplementary angles are in the ratio 3: 2. Find the measure of the smaller angle.

• A. ${85}^o$
• B. ${72}^o$
• C. ${47}^o$
• D. ${68}^o$

Answer 1

The correct option is B ${72}^o$

Given: Two supplementary angles are in the ratio 3:2.

Let the supplementary angles be 3x and 2x.

We know that supplementary angles add up to ${180}^{\circ }$.

$\Rightarrow 3x+2x={180}^{\circ }$

$\Rightarrow 5x={180}^{\circ }$

$\Rightarrow x={36}^{\circ }$

$\Rightarrow 2x={72}^{\circ }$

$\therefore$ The measure of the smaller angle is ${72}^{\circ }$.