Question

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the larger angle is:

• A. ${72}^o$
• B. ${108}^o$
• C. ${36}^o$
• D. ${54}^o$

Answer 1

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

Let the complementary angles be $x$ and $({90}^o-x)$.

Then, $2x=3({90}^o-x)$
$\Rightarrow$ $2x={270}^o-3x$ $\Rightarrow$ $5x={270}^o$
$\Rightarrow$ $x=\frac{{270}^o}{5}={54}^o$
$\therefore$ The two angles are ${54}^o$ , ${36}^o$