---
title: "Angle Sum Rules"
description: "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"
canonical: https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L
source: https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L.md
retrieved: 2026-10-19
---

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# 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

Subject: Mathematics · Area: Geometry · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L

## Ready when they can

- 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

## Lesson: Angles that add up

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°.

*(drawing: Spin around one point and stop partway. A half turn makes a straight line, and a full turn brings you back to the start.)*

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.

**Example.** 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°.

**Tip.** 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°.

**Recap.** Straight line angles add to 180°, angles around a point add to 360°, and vertically opposite angles match.

## Practice

16 questions on this page, each with its working shown.

## Needs first

- [Geometric diagram conventions](https://lightmysky.com/learn/mathematics/geometric-diagram-conventions-mt_e4V6hvcuEJ)
- [Degrees and turns](https://lightmysky.com/learn/mathematics/degrees-and-turns-mt_qUGMyMYn9m)

## Opens up

- [Angles that add up on a diagram](https://lightmysky.com/learn/mathematics/angles-that-add-up-on-a-diagram-mt_89riIKwGYp)
- [Pie charts and line graphs](https://lightmysky.com/learn/mathematics/pie-charts-and-line-graphs-mt_bESTSBB0wK)
- [Angles in triangles (age 10+)](https://lightmysky.com/learn/mathematics/angles-in-triangles-age-10-mt_cdMlC7EpTJ)
- [Fractions, Decimals & Percentages](https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ)
- [Understanding angles (age 10+)](https://lightmysky.com/learn/mathematics/understanding-angles-age-10-mt_QDTO3GAgcq)
- [Understanding angles (age 11+)](https://lightmysky.com/learn/mathematics/understanding-angles-age-11-mt_tedML_iu4Y)