---
title: "Angles that add up on a diagram"
description: "Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown"
canonical: https://lightmysky.com/learn/mathematics/angles-that-add-up-on-a-diagram-mt_89riIKwGYp
source: https://lightmysky.com/learn/mathematics/angles-that-add-up-on-a-diagram-mt_89riIKwGYp.md
retrieved: 2026-09-02
---

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# Angles that add up on a diagram

Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown

Subject: Mathematics · Area: Geometry · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/angles-that-add-up-on-a-diagram-mt_89riIKwGYp

## Ready when they can

- Two angles on a straight line are 65° and x°; find x = 115°
- An angle is decomposed into 35° and 40°; state the whole angle is 75°
- Solve: angles at a point are 120°, 90°, and x°; find x = 150°

## Lesson: Finding a Missing Angle

You already know that angles on a straight line add up to 180 degrees, and angles all the way around a point add up to 360 degrees. Now you can use those facts to find an angle you don't know yet. Give the missing angle a letter, like x, and write an equation. Then solve it.

*(drawing: This angle splits into two parts: 25° and 30°. Add the parts to get the whole angle: 25 + 30 = 55°.)*

Angle measure adds up. When an angle is split into parts, the parts add together to make the whole angle. Turn that around and you get a missing part: whole angle minus the part you know. Watch which total you use. If the whole angle is given to you, that number is the total, not 180 and not 360.

**Example.** Two angles sit next to each other on a straight line. One angle is 40°, and the other is x°. Since the two angles together make a straight line, write 40 + x = 180. Subtract 40 from both sides: x = 140°.

**Example.** Three angles meet at a point. Two of them are 130° and 140°, and the third is x°. Angles all the way around a point add to 360, so write 130 + 140 + x = 360. That is 270 + x = 360, so x = 90°.

**Tip.** When an angle is missing, first find the total: 180° for a straight line, 360° for angles around a point. Then subtract the angles you already know. What's left over is your missing angle.

**Recap.** Give the unknown angle a letter, write an equation using the total, and solve for it.

## Practice

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

## Needs first

- [Measuring angles](https://lightmysky.com/learn/mathematics/measuring-angles-mt_4MFUAsbx_6)
- [Geometric diagram conventions](https://lightmysky.com/learn/mathematics/geometric-diagram-conventions-mt_e4V6hvcuEJ)
- [Angle Sum Rules](https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L)
- [Two-Step Equations](https://lightmysky.com/learn/mathematics/two-step-equations-mt_anAe11HAEH)

## Opens up

- [Building and critiquing a mathematical argument](https://lightmysky.com/learn/mathematics/building-and-critiquing-a-mathematical-argument-mt_2ESZh70NyS)
- [Understanding angles (age 10+)](https://lightmysky.com/learn/mathematics/understanding-angles-age-10-mt_QDTO3GAgcq)