Angles & Symmetry (Year 4–5) (Years 4–5) — Maths

An angle measures a turn. Learn right, acute and obtuse angles, quarter and half turns, and lines of symmetry.

An angle is a measure of turn. When you spin around, or open a door, or turn a page, you are making an angle. The more you turn, the bigger the angle.

Why this matters: Angles are everywhere — the corner of a book, the hands of a clock, the way a door swings open. Symmetry is everywhere too, from a butterfly's wings to the beautiful tile patterns in a mosque.

Types of angle

A right angle is a quarter turn. It measures 90°. The corner of a book or a table is a right angle.

Angle	Size	Looks like
Acute	Smaller than 90°	A narrow, sharp corner
Right angle	Exactly 90°	A square corner
Obtuse	Bigger than 90° (but less than 180°)	A wide, open corner

Turns

A quarter turn is 90° (a right angle). A half turn is 180° (a straight line, facing the opposite way). A full turn is 360° (all the way round, back to the start).

Think of a clock: from 12 to 3 is a quarter turn (90°). From 12 to 6 is a half turn (180°). All the way back to 12 is a full turn (360°).

Put these turns in order, smallest first:

Quarter turn (90°)
Half turn (180°)
Full turn (360°)

Lines of symmetry

A shape has a line of symmetry if you can fold it so both halves match exactly, like a mirror. A square has 4 lines of symmetry. A butterfly has 1. Many beautiful Islamic tile patterns are symmetric — you can fold them and the two halves match perfectly, which is part of what makes them so pleasing to look at.