Question

Which of the following pairs of angles are supplementary?

• A. $65°,115°$
• B. $63°,27°$
• C. $112°,68°$
• D. $130°,50°$
• E. $45°,45°$
• F. $80°,10°$

Answer 1

Answer: (A), (C), (D)

$130°,50°$

Step 1. Explanation for the correct option.

If the sum of two angles is $180°$, then they are called supplementary angles.

sum of the angles

$$\begin{gathered} =65°+115° \\ =180° \end{gathered}$$

sum of the angles

$$\begin{gathered} =112°+68° \\ =180° \end{gathered}$$

sum of the angles

$$\begin{gathered} =130°+50° \\ =180° \end{gathered}$$

Hence angles $65°,115°$, $112°,68°$ and $130°,50°$ are supplementary.

Step 2. Explanation for the correct options.

sum of the angles

$$\begin{gathered} 63°+27°=90° \\ 45°+45°=90° \\ 80°+10°=90° \end{gathered}$$

So, these angles are not supplementary.

Hence, the correct options are $\mathrm{A},\mathrm{C}\mathrm{and}\mathrm{D}$.