Question

If the supplement of an angle is two-third of itself. Determine the angle and its supplement.

Answer 1

Let required angle =x
Then its supplement angle= ${180}^{\circ }-x\therefore ({180}^{\circ }-x)=\frac{2}{3}x{540}^{\circ }-3x=2x\Rightarrow 2x+3x={540}^{\circ }\Rightarrow 5x={540}^{\circ }\Rightarrow x=\frac{{540}^{\circ }}{5}={108}^{\circ }$
$\therefore$ Supplement angle = ${180}^{\circ }-{108}^{\circ }={72}^{\circ }$