Two complementary angles are such that twice the measure of one is equal to three times the measure of the other.
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°

Solution:

(b) 54°

Let the measure of the required angle be $x^{\circ}$

Then, the measure of its complement will be $(90-x)^{\circ}$.

$\therefore 2 x=3(90-x)$

$\Rightarrow 2 x=270-3 x$

$\Rightarrow 5 x=270$

$\Rightarrow x=54$

 

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