Question

Find the angle which is twice its supplement.

Answer 1

Compute the required angle:

Two angles are called supplementary angles if their sum is equal to ${180}^{\circ }$.

Suppose, $x$ be the angle which is twice its supplement.

Therefore, another supplement angle is $\frac{x}{2}$. Then,

$\begin{array}{rcl}x+\frac{x}{2}& =& {180}^{\circ }\end{array}$

$\frac{2x+x}{2}=180°$

$$\begin{gathered} \frac{3x}{2}=180° \\ 3x=360° \end{gathered}$$

$$\begin{gathered} x=\frac{360}{3} \\ x=120° \end{gathered}$$

Therefore, the angle which is twice its supplement is ${120}^{\circ }$.