Question

Question 15
The measure fo an angle which is four times its supplement, is
(a) ${36}^{\circ }$
(b) ${144}^{\circ }$
(c) ${16}^{\circ }$
(d) ${64}^{\circ }$

Answer 1

Let the required angle be x then its supplement will be $({180}^{\circ }-x)$.
It is given that, the angle is four times its supplement.
therefore $x=4({180}^{\circ }-x)\Rightarrow x=4\times {180}^{\circ }-4x\Rightarrow x+4x={720}^{\circ }\Rightarrow 5x={720}^{\circ }\Rightarrow x=\frac{{720}^{\circ }}{5}\Rightarrow x={144}^{\circ }$