---
title: "Angles in triangles (age 10+)"
description: "Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties"
canonical: https://lightmysky.com/learn/mathematics/angles-in-triangles-age-10-mt_cdMlC7EpTJ
source: https://lightmysky.com/learn/mathematics/angles-in-triangles-age-10-mt_cdMlC7EpTJ.md
retrieved: 2026-10-19
---

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# Angles in triangles (age 10+)

Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties

Subject: Mathematics · Area: Geometry · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/angles-in-triangles-age-10-mt_cdMlC7EpTJ

## Ready when they can

- Find a missing angle in a triangle given two angles (using angle sum = 180°)
- Calculate a missing angle in a quadrilateral (angle sum = 360°)
- Calculate the interior angle of a regular hexagon from the angle sum formula

## Lesson: Angles in triangles and other shapes

You already know how to classify shapes by their sides and angles, and that angles come in different sizes. Now you can use angles as clues to solve puzzles. Every triangle's three angles add up to exactly 180°. If you know two of them, you can find the third one without measuring anything.

*(drawing: A triangle's three angles always total 180°, no matter its size or shape.)*

**Example.** Two angles in a triangle are 55° and 70°. Add them: 55° + 70° = 125°. Then subtract from 180°: 180° - 125° = 55°. The third angle is 55°.

A quadrilateral's four angles always add up to 360°. You can see why by splitting it into two triangles: 180° + 180° = 360°. Regular polygons with more sides follow the same pattern. A regular hexagon has six equal angles that add up to 720° in total.

**Tip.** To find one angle in a regular polygon, divide the total angle sum by the number of angles. For a regular hexagon: 720° ÷ 6 = 120° for each angle.

**Recap.** Add up the angles you already know, subtract from the shape's total, and what's left is the missing angle.

## Practice

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

## Needs first

- [Geometric diagram conventions](https://lightmysky.com/learn/mathematics/geometric-diagram-conventions-mt_e4V6hvcuEJ)
- [Classifying shapes by properties](https://lightmysky.com/learn/mathematics/classifying-shapes-by-properties-mt_liIW336odh)
- [Angle Sum Rules](https://lightmysky.com/learn/mathematics/angle-sum-rules-mt_oqziWKry-L)

## Opens up

- [Generalising with repeated reasoning](https://lightmysky.com/learn/mathematics/generalising-with-repeated-reasoning-mt_iyovKgZC1q)
- [Angle sums in triangles and polygons](https://lightmysky.com/learn/mathematics/angle-sums-in-triangles-and-polygons-mt_J03RFlVdas)
- [Constructing mathematical arguments](https://lightmysky.com/learn/mathematics/constructing-mathematical-arguments-mt_j5YqQnN6xe)