--- title: "Understanding angles (age 10+)" description: "Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties" canonical: https://lightmysky.com/learn/mathematics/understanding-angles-age-10-mt_QDTO3GAgcq source: https://lightmysky.com/learn/mathematics/understanding-angles-age-10-mt_QDTO3GAgcq.md retrieved: 2026-10-19 --- > **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`. # Understanding angles (age 10+) Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties Subject: Mathematics · Area: Geometry · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/understanding-angles-age-10-mt_QDTO3GAgcq ## Ready when they can - Find a missing angle at a point given the other angles in a full-turn partition with no gaps or overlaps. Use equal-part division when parts are stated equal. - Use the straight-angle property (angles exactly filling a straight angle sum to 180°) to find an unknown angle. - Identify vertically opposite angles and use the property that they are equal to find unknowns. Use equal splitting of a computed neighbour. ## Lesson: Angles at a point, on a line, and across a cross Angles can meet at a single point and fill all the space around it. When they fill that whole space with no gaps or overlaps, they add up to 360 degrees, a full turn. Angles can also sit side by side along a straight line. When two angles exactly fill a straight angle with no gaps or overlaps, they add up to 180 degrees. *(drawing: A full turn around a point is 360 degrees. One quarter turn is 90 degrees.)* Two angles exactly filling a straight angle with no gaps or overlaps add up to 180 degrees. This works for any exact partition of a straight angle, not only two angles. Two straight lines cross and make four angles. The angles across from each other share the same vertex but no ray. They are called vertically opposite angles. They are always equal. Adjacent angles share a ray and exactly fill a straight angle, so they add to 180. **Example.** Two straight lines cross. One angle is 70 degrees. The angle vertically opposite it is also 70 degrees. The angle next to it on the straight angle is 180 - 70 = 110 degrees. The angle opposite that is also 110 degrees. One known angle unlocks all four. **Example.** Three angles fill one full turn with no gaps or overlaps. One is 90 degrees and the other two are equal. Subtract: 360 - 90 = 270. Divide: 270 / 2 = 135 degrees each. Two straight lines cross. One opening is 50 degrees, so its neighbour on the straight line is 180 - 50 = 130 degrees. A ray splits that neighbour into two equal parts. Divide: 130 / 2 = 65 degrees each. To find a missing angle, first identify the relationship. If two angles are vertically opposite, copy the equal measure. If angles exactly fill a straight angle, subtract the known parts from 180. If they fill one full turn, subtract from 360. If remaining parts are equal, divide the remainder equally. Adding all parts back checks a partition. For vertically opposite angles, equality checks the opposite measures. **Recap.** Angles filling one full turn add to 360. Angles exactly filling a straight angle add to 180. Vertically opposite angles are equal. Use one known angle to find all four at a crossing. ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Angles that add up on a diagram](https://lightmysky.com/learn/mathematics/angles-that-add-up-on-a-diagram-mt_89riIKwGYp) - [Angle Sum Rules](https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L) ## Opens up - [Understanding angles (age 11+)](https://lightmysky.com/learn/mathematics/understanding-angles-age-11-mt_tedML_iu4Y)