Angle Relationships
Complementary angles add to 90° and supplementary angles to 180°.
About this topic
Pairs of angles can be related. Complementary angles add up to 90°, supplementary angles add up to 180°, and vertical angles formed by intersecting lines are equal. Adjacent angles share a side and vertex, and a linear pair is adjacent angles forming a straight line.
These relationships let you set up equations to find unknown angles. They are the first tools used in geometric proofs and underlie all later results on triangles and parallel lines.
Worked example: two lines cross, and one of the four angles is 70°. Its vertical angle is also 70°, and each neighbour forms a linear pair with it, so those are 110°. If two angles are complementary and one is twice the other, then 3x = 90 and the angles are 30° and 60°. Setting up and solving such equations is the main skill.
These ideas appear in the design of street intersections, folding screens and scissors. A common error is mixing up complementary and supplementary; a memory trick is C comes before S as 90 comes before 180. Another is assuming that adjacent angles are always supplementary, but that is true only for a linear pair. Equal angles in a diagram must be justified by a theorem and not just by how the picture looks, since diagrams are not always drawn to scale.
Key ideas
- Vertical angles are equal
- Linear pairs are supplementary
- Use algebra to find missing angles
Quick check
Use cases: where Angle Relationships helps
- Homework: review the key idea behind Angle Relationships before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Angle Relationships without notes.
- Visual learning: play with the interactive lab to see how Angle Relationships changes when you adjust its inputs.
- Teaching a friend: explain Angle Relationships in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Angle Relationships?
Complementary angles add to 90° and supplementary angles to 180°.
What will I learn in Angle Relationships?
Vertical angles are equal. Linear pairs are supplementary. Use algebra to find missing angles.
Is Angle Relationships part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Angle Relationships lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Angle Relationships?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.