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 $(90-x)^{\circ}$.
$\therefore 2 x=3(90-x)$
$\Rightarrow 2 x=270-3 x$
$\Rightarrow 5 x=270$
$\Rightarrow x=54$