Vertically Opposite Angles
When two straight lines cross, the opposite angles are equal. These are called vertically opposite angles.
When two straight lines intersect, they create two pairs of vertically opposite angles. Each pair is equal.
Why does this work? Look at one pair of adjacent angles. They sit on a straight line, so they add up to . The angle opposite shares a straight line with the same neighbour, so it must also be minus that neighbour. Both opposite angles therefore have the same value.
If one angle is , the angle next to it is , and the angle opposite is also .
Select "Vert. opposite" and adjust the angle. Notice how the opposite angles always stay equal, and adjacent angles always sum to .
Watch it work
Question: Two straight lines cross. One angle is . Find the other three angles.
Step 1: The angle vertically opposite to is also .
Step 2: The adjacent angle is on a straight line with , so it is .
Step 3: The remaining angle is vertically opposite to , so it is also .
Check: . Correct (angles at a point).
Have a go
Q1. Two lines cross. One angle is . What is the vertically opposite angle?
(vertically opposite angles are equal).
Q2. Two lines cross. One angle is . Find the other three angles.
Opposite angle: . Adjacent angle: . Its opposite: .
The four angles are .
Q3. Two lines cross. The angles are and (adjacent). Find .
Adjacent angles on a straight line: , so .
. The four angles are .
Q4. A student says vertically opposite angles add up to . Is this always true?
No. Vertically opposite angles are equal, not supplementary. They only add up to if each is . It is adjacent angles that sum to .