Vertical Angles
Opposite angles formed by intersecting lines are equal.
Key idea
Opposite angles formed by intersecting lines are equal.
In depth
When two lines cross, the angles opposite each other are equal. This is because each is supplementary to the same neighbouring angle, so they must match.
Worked example
Two lines cross and one angle is 65°. The opposite angle is 65°, and the two others are each 115°.
Real-world uses
- Checking that crossing roads or railway tracks meet at equal angles
- Sightlines in surveying
Common mistake
Assuming adjacent angles are equal; only the opposite ones are.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Vertical Angles?
Opposite angles formed by intersecting lines are equal. It is a topic at the intermediate level in Geometry.
Where is Vertical Angles used in real life?
Real-world examples: Checking that crossing roads or railway tracks meet at equal angles; Sightlines in surveying.
What should I learn before Vertical Angles?
Make sure you are comfortable with Complementary and Supplementary, the previous topic in Geometry.
What is a common mistake with Vertical Angles?
Assuming adjacent angles are equal; only the opposite ones are.
How can I practise Vertical Angles?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Vertical Angles?
Move on to Parallel Lines and Transversals next.
Related intermediate topics in Geometry
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.
- Pythagorean Theorem – In a right triangle the squares on the legs sum to the square on the hypotenuse.