The measure of an angle is five times its complement. The angle measures

Question:

The measure of an angle is five times its complement. The angle measures
(a) 25°
(b) 35°
(c) 65°
(d) 75°

Solution:

(d) $75^{\circ}$

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

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

$\therefore x=5(90-x)$

$\Rightarrow x=450-5 x$

$\Rightarrow 6 x=450$

$\Rightarrow x=75$

 

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