Question

When two lines intersect at a point, what is the sum of the measures of both pairs of vertical angles?

• A. ${90}^o$
• B. ${180}^o$
• C. ${360}^o$
• D. None of the above

Answer 1

The correct option is C ${360}^o$

We will draw a figure of two lines $AC$ and $BD$ intersecting at point $O$.
We can observe from the figure that two pairs of vertical angles are formed.
$\bullet$ $\angle 1$ and $\angle 3$
$\bullet$ $\angle 2$ and $\angle 4$
Now, the sum of the measures of both the pairs, i.e.
$\angle 1+\angle 3+\angle 2+\angle 4$
= $\angle 1+\angle 2+\angle 3+\angle 4$
Which forms a full circle.

We know that a full circle is equal to ${360}^o$.

Hence, option(c.) is correct.