Understanding angles (age 10+)
Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties
What a learner can do afterwards
- Find a missing angle at a point given the other angles (total 360°)
- Use the straight-line property (angles sum to 180°) to find an unknown angle
- Identify vertically opposite angles and use the property that they are equal to find unknowns
The lesson
Angles can meet at a single point, filling all the space around it, like a fan opening all the way. When they fill that whole space, they add up to 360 degrees, a full turn.
Angles can also sit side by side along a straight line. Two angles like that always add up to 180 degrees, half a turn. If you know one angle, subtract it from 180 to find the other.
Two straight lines cross and make an X shape. This makes four angles. The angles across from each other, on opposite sides of the X, are called vertically opposite angles, and they are always equal. If one angle is 70 degrees, the angle directly across from it is also 70 degrees.
Before you calculate, ask what kind of angles you have: do they go all the way around a point (360°), sit on a straight line (180°), or sit across from each other where two lines cross (equal)?
Angles at a point add to 360°, angles on a straight line add to 180°, and vertically opposite angles are always equal.
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.