Question

Two complementary angles are such that twice the measure of one is equal to three times the measure of the other. The measure of larger angle is
(a) 72°
(b) 54°
(c) 63°
(d) 36°

Answer 1

(b) 54°

Let the measure of the required angle be $x°$.
Then, the measure of its complement will be$\left(90-x\right)°$.
$$\begin{gathered} \mathbf{\therefore }2x=3\left(90-x\right) \\ \Rightarrow 2x=270-3x \\ \Rightarrow 5x=270 \\ \Rightarrow x=54 \end{gathered}$$