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
The lesson
When two angles sit side by side on a straight line, 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.
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°.
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.
Watch it
Where it sits
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.