Geometry

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# 1.3.4 Vertically opposite angles

When two straight lines cross, they form four angles. In the diagram below, these angles are labelled α, β, θ and φ and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called vertically opposite angles. Here α and β are a pair of vertically opposite angles, as are θ and φ. Although such angles are called ‘vertically opposite’, they do not need to be vertically above and below each other!

## Activity 3: Vertically opposite angles

Click here [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] for Activity 3.

For two intersecting straight lines, vertically opposite angles are equal.

We can show that vertically opposite angles are equal as follows:

α and θ lie on a line.

So, α + θ = 180°

and α = 180° – θ

but β and θ also lie on a line.

So, β + θ = 180°

and β = 180° – θ.

Hence, α = β because they are both equal to 180° – θ.

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