Question

An angle is equal to five times its complement. Determine its measure. [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

Let the measure of the given angle be x degrees.

Then, its complement is $(90–x{)}^{\circ }$.

$Angle=5\times Itscomplement$

$\Rightarrow x=5\times ({90}^{\circ }–x)$

$\Rightarrow x={450}^{\circ }–5x$

$\Rightarrow 6x={450}^{\circ }$

$\Rightarrow x={75}^{\circ }$

Thus, the measure of the given angles is ${75}^{\circ }$.