Question

Question 56

Fill in the blanks to make the statement true.

An angle which is half of its supplement is of ___

Answer 1

Let the required angle be x then its supplement will be $({180}^{\circ }-x)$
It is given that x is the half of its supplement i.e. $({180}^{\circ }-x)$
Therefore $x=\frac{1}{2}\times ({180}^{\circ }-x)\Rightarrow 2x={180}^{\circ }-x\Rightarrow 2x+x={180}^{\circ }\Rightarrow 3x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{3}\Rightarrow x={60}^{\circ }$