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You already know a full turn is 360 degrees, like spinning all the way around and facing the start again. A round pie is cut into three slices that all meet at the center point.
How many degrees do all three slices add up to?
Angle Sum Rules
Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles
What a learner can do afterwards
- State that two angles on a straight line add to 180°
- Explain that four right angles at a point make 360°
- Identify 270° as three right angles
1 · Read
Think of a book lying open flat on a table, its two covers forming one straight line. When two angles sit side by side on a straight line like that, they always add up to 180°. A straight line is half of a full turn, so its angles share that half.
When angles meet at one point and go all the way around it, they add up to 360°, a whole turn. Four right angles fit exactly around a single point, because 90° + 90° + 90° + 90° = 360°.
When two straight lines cross, they make two pairs of angles across from each other. Each pair is called vertically opposite angles, and the two angles in a pair are always equal.
Try it together
Three angles meet at a point: 150°, 100°, and one more angle. All the angles at a point add up to 360°, so add the two known angles first: 150° + 100° = 250°. Then subtract from 360°: 360° − 250° = 110°. The missing angle is 110°.
Good to know
After you find a missing angle, add all the angles back together to check. On a straight line the total should be 180°. Around a point it should be 360°.
Straight line angles add to 180°, angles around a point add to 360°, and vertically opposite angles match.
2 · Watch
3 · Play
Take it off screen
Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
Then practise
16 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.