Geometry
Geometry

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Geometry

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.

MU120_4M7

For further information, take a look at our frequently asked questions which may give you the support you need.

Have a question?
Free Courses

OpenLearn has over 800 free courses across all our subjects designed by our academic experts. From 1 to 100 hours, introductory to advanced, you can start learning at any time and all for free.