Question

Angles that are both supplementary and vertically opposite are

• A. $95°,85°$
• B. $90°,90°$
• C. $100°,80°$
• D. $45°,45°$

Answer 1

The correct option is B

$90°,90°$

We know that two angles are said to be supplementary angles if the sum of their measures is $180°$.

Let's consider one angle is $\mathrm{x}°$.

Then another angle is also $\mathrm{x}°$. (Since both the angles are vertically opposite angles and vertically opposite angles are equal to each other.)

Now $\mathrm{x}°+\mathrm{x}°=180°$ (Since both the angles are supplementary angles)

$$\begin{gathered} \Rightarrow 2\mathrm{x}°=180° \\ \Rightarrow \mathrm{x}°=\frac{180°}{2} \\ \Rightarrow \mathrm{x}°=90° \end{gathered}$$

Hence the required angles are $90°,90°$

Therefore option (B) is correct.