Angles in Year 6

In Year 6 you'll meet angles in a much more grown-up way. You'll learn to classify them by size, measure them precisely with a protractor, work out angle sums in triangles and quadrilaterals, and recognise pairs of angles at intersecting lines.

Types of angles by size

You can remember a right angle as the corner of a sheet of paper. An acute angle is "sharper" than right, an obtuse one is "more open".

Measuring with a protractor

A protractor is a semicircular tool with numbers from 0° to 180°. The procedure:

1. Place the vertex of the angle on the centre of the protractor (the black dot).
2. Align one arm of the angle with the zero line (the flat side of the protractor).
3. The other arm crosses the protractor at a number — that's the measure of the angle.

You'll practise on a protractor in 10° steps (from 20° to 160°).

Angle sum in a triangle

In every triangle:

α + β + γ = 180°

So if you know two angles, you work out the third:

60° + 70° = 130°

180° − 130° = 50°

The 180° sum is universal — it holds for acute, right and obtuse triangles alike.

Angle sum in a quadrilateral

Any quadrilateral can be split into two triangles by a diagonal. So:

α + β + γ + δ = 360° (two triangles × 180°)

The method is the same: add three angles, subtract from 360°.

Vertical and supplementary angles

When two lines cross, they create four angles. They form two pairs of equal-size angles:

• Vertical angles sit across the vertex of the intersection. They are always equal.
• Supplementary angles sit on the same straight line (right next to each other). Together they always make 180°.

If the given angle is 60°, the vertical angle is also 60°, and the supplementary angle is 180° − 60° = 120°.

What you will learn next

• Classify an angle by its measure — name the type.
• Measure an angle with a protractor — read off the measure.
• Angle sum in a triangle — find the third angle.
• Vertical and supplementary angles — pairs at intersections.
• Angle sum in a quadrilateral — find the fourth angle.