Question

If two lines intersect at a point, then the vertically opposite angles are always _____________.

Answer 1

If two lines intersect at a point, then the vertically opposite angles are always equal.

When two lines intersect at any point, the vertically opposite angles are equal and are known as vertical opposite

angles.

This is because any two pairs of adjacent angles will be supplementary pairs.

$$\begin{gathered} \angle 1+\angle 2=180° \\ \Rightarrow \angle 2=180°-\angle 1 \end{gathered}$$

Again,

$$\begin{gathered} \angle 3+\angle 2=180° \\ \Rightarrow \angle 2=180°-\angle 3 \end{gathered}$$

Therefore,

$$\begin{gathered} \angle 2=180°-\angle 1=180°-\angle 3 \\ \therefore \angle 1=\angle 3 \end{gathered}$$

Similarly, $\angle 2=\angle 4$

Hence, the required answer is that vertically opposite angles are equal.