Question

If a and B are supplementary and vertical angles what is MB

Answer 1

Solution:

Given the;

Two angles ∠A and ∠B are supplementary and vertical angles.

When angles are supplementary, they add up to 180°

Vertical angles are equal, and since,

$\begin{gathered} m\angle A+m\angle B=180\degree\text{ \lparen supplementary angles\rparen} \\ m\angle A=m\angle B\text{ \lparen vertical angles\rparen} \end{gathered}$

Then,

$\begin{gathered} m\angle B+m\angle B=180\degree \\ 2(m\angle B)=180\degree \\ Divide\text{ both sides by 2} \\ \frac{2(m\angle B)}{2}=\frac{180\degree}{2} \\ m\angle B=90\degree \end{gathered}$

Hence, ∠B is 90°s