G1GeometryFoundation

Angles

Angle questions appear on every paper. A handful of rules — angles on a line, around a point, in triangles, and in parallel lines — let you find almost any missing angle.

40 min Video by Maths Genie AQA GCSE Maths

AnglesWatch the walkthrough, then read the notes below.

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What you'll learn

Use angles on a line and around a point
Find angles in triangles and quadrilaterals
Use angles in parallel lines
Find interior and exterior angles of polygons

The basic angle rules

Angles on a straight line add to $180°$ . Angles around a point add to $360°$ . Angles in a triangle add to $180°$ , and in a quadrilateral to $360°$ .

line = 180°, point = 360°, △ = 180°

Learn these by heart.

Parallel lines and polygons

When a line crosses two parallels: $corresponding$ angles (F-shape) are equal, $alternate$ angles (Z-shape) are equal, and $co-interior$ angles (C-shape) add to $180°$ . For any polygon, the exterior angles add to $360°$ .

exterior angle = \frac{360°}{n}

For a regular polygon with n sides.

1A hexagon has 6 sides.

360° \div 6 = 60°

Answer

60°

Tip — Interior + exterior angle = 180° at each corner of a polygon.

Remember these

angles in a triangle = 180°

Triangle rule.

sum of interior angles = (n - 2) \times 180°

Polygon with n sides.

exterior angle = \frac{360°}{n}

Regular polygon.

Watch out for these

Mixing up alternate and co-interior angles.

Alternate (Z) are equal; co-interior (C) add to 180°.

Using 360° for the angles in a triangle.

A triangle’s angles add to 180°.

Key takeaways

Line = 180°, point = 360°, triangle = 180°.
Parallel lines: corresponding & alternate equal; co-interior add to 180°.
Exterior angles of any polygon add to 360°.

Test yourself

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