--- 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: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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 exactly filling a straight angle are 65° and x°; find x = 115° - Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown - Three angles exactly filling one full turn are 120°, 90°, and x°; find x = 150° ## Lesson: Finding a Missing Angle Angles on a straight line add to 180 degrees when they sit side by side and exactly fill the straight angle with no gaps or overlaps. Angles around a point add to 360 degrees when they fill one full turn with no gaps or overlaps. A given whole angle may measure 90, 115, 130, 150 or 200 degrees. To find a missing part, add the known parts, then subtract from the given whole. *(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 that exactly fill it with no gaps or overlaps, the parts add together to make the whole angle. To find a missing part, subtract the known part from the whole. Watch which total you use. If the whole angle is given, that number is the total, whether it is 90, 115, 130, 150, 200 or any other value. **Example.** Two angles sit side by side on a straight line, exactly filling it. One angle is 40°, and the other is x°. Write 40 + x = 180. Subtract 40 from both sides: x = 140°. Check: 40 + 140 = 180. **Example.** Three angles meet at a point and fill one full turn with no gaps or overlaps. Two are 130° and 140°, and the third is x°. Write 130 + 140 + x = 360. That is 270 + x = 360, so x = 90°. Check: 130 + 140 + 90 = 360. To find a missing angle, first find the total: 180° for a straight angle, 360° for angles filling one full turn, or the given whole angle. Then subtract the angles you already know. What is left is your missing angle. Check by adding all the parts back together. For example, if you found x = 140 from 40 + x = 180, check: 40 + 140 = 180. **Recap.** Give the unknown angle a letter, write an equation using the total, solve for it, then check by adding the parts back. ## 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) - [Two-Step Equations](https://lightmysky.com/learn/mathematics/two-step-equations-mt_anAe11HAEH) - [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) ## 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)