---
title: "Angle sums: cheat sheet"
subtitle: "Angles and shapes"
---

# Angle sums

> The words and methods from this unit, with an example of each.

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**interior angle**: An angle inside a shape, at one of its corners.

$$\angle A$$

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**polygon**: A closed shape with straight sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), octagon (8).

$$n \text{ sides}, \; n \text{ corners}$$

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**regular polygon**: All sides and all angles are equal, so each angle is the angle sum shared equally: a regular hexagon has angles of $120^\circ$.

$$\text{each angle} = \dfrac{(n - 2) \times 180^\circ}{n}$$

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**angle sum of a triangle**: True for every triangle, whatever its shape or size: tear off the corners and they fill a straight line.

$$a + b + c = 180^\circ$$

_An obtuse triangle: 24° + 127° + 29° = 180°_

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**angle sum of a polygon**: Split it into triangles from one corner: a shape with $n$ sides makes $n - 2$ triangles. A pentagon: $3 \times 180^\circ = 540^\circ$.

$$(n - 2) \times 180^\circ$$

_A pentagon splits into 3 triangles from A: 540°_

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