Question

If two supplementary angles are in the ratio $1:2,$ then the bigger angle is

• A. ${120}^{\circ }$
• B. ${125}^{\circ }$
• C. ${110}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A

${120}^{\circ }$

The Explanation for the correct answer.

As the ratio of the angles is $1:2,$ then let the two angles be$1x$ and $2x.$

Now since the angles are supplementary, their sum is ${180}^{\circ }$

$$\begin{gathered} \Rightarrow 1x+2x={180}^{\circ } \\ \Rightarrow 3x=180 \\ \Rightarrow x=\frac{{180}^{}}{3} \\ \Rightarrow x={60}^{\circ } \end{gathered}$$

Then the bigger angle is $2x=2\times {60}^{\circ }={120}^{\circ }$

Hence, Option(A) is the correct answer.