What are vertically opposite angles? (or vertical angles). Angles on intersecting lines.

If you have 2 straight lines that intersect at a point, then the angles opposite each other are the same. These type of angles are called vertically opposite angles in the UK or vertical angles in the US.

Example 1

Work out angles x, y and z. Give reasons for each answer.

Angle x is equal to 43⁰ as angle x is opposite the 43⁰ angle (vertically opposite angles are equal).

Now since the angle around a point add up to 360⁰, then angles y and z can be found by subtracting the two 43⁰ angles from 360⁰ and halving your answer.

Therefore:

360 – 43 – 43 = 274⁰.

And 274⁰ ÷ 2 = 137⁰.

So angles y and z are 137⁰.

You can confirm your angles are correct by seeing if they add up to 360⁰

43 + 43 + 137 + 137 = 360⁰.

A quicker way to find angles y and z is to just take the 43⁰ from 180⁰ (as angles on a straight line add up to 180⁰) So 180 – 43 = 137⁰.

Either way will be acceptable in an exam situation.

Example 2

The diagram shows two intersecting lines. Calculate angles m and n. Explain your answers.

Angle m is equal to 109⁰ as angle m is opposite the 109⁰ angle (vertically opposite angles are equal).

Like example 1, angle n can be found by subtracting the two 109⁰ angles from 360⁰ and halving your answer.

Therefore:

360 – 109 – 109 = 142⁰.

And 142⁰ ÷ 2 = 72⁰

So angle n is equal to 71⁰.

Again you can check that all the angles add to 360⁰

71 + 71 + 109 + 109 = 360⁰.

Alternatively, you could just take the 109 off 180 to give 71 as angles on a straight line add up to 180.