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11+ Maths Guide · Year 5–6 · Free lesson

Angles on a Line and at a Point

Two totals — 180° on a line, 360° around a point — solve a huge share of angle questions. This lesson drills the subtract-from-the-total routine with the classic exam variations.

G10Angles on a Line and at a Point
180° on a line, 360° round a point.
Angles that sit together on a line or around a point have fixed totals.
Two totals to remember.
ab
On a straight line: a + b = 180°
Around a point: angles total 360°
Missing angle = total − the angles you know.
1

Learn the 2 Facts

1Angles on a straight line: 180°.

Two or more angles sitting on a line add to 180°.

a + b = 180°

2Angles around a point: 360°.

A full turn — all the angles meeting at a point add to 360°.

total 360°

3Subtract to find the missing one.

On a line with 115° known: 180 − 115 = 65°.

180 − 115 = 65
💡 Key IdeaThese two facts solve half of all KS2 angle problems — find the total, subtract what you know.
2

Worked Example

Find each missing angle.

On a line, one angle is 115°
180 − 115 = 65
65°
Around a point: 140° and 90° known
360 − 230 = 130
130°
Three equal angles on a line
180 ÷ 3 = 60
60° each
3

Watch Out! Common Mistakes

✕
Using 360° for a straight line.
line: 360 − 115 = 245° ✕

Wrong total! A straight line is half a turn: 180°. Answer: 65°.

✕
Only subtracting one known angle.
360 − 140 = 220° ✕

Subtract them all! 360 − 140 − 90 = 130°.

✕
Angles not actually on the line.

Check the diagram! The 180° rule only applies to angles sitting together on the straight line at the same point.

⬇ Cheat Sheet

ANGLES ON A LINE AND AT A POINT
  1. Straight line total: 180°.
  2. Around a point total: 360°.
  3. Missing angle = total − known angles.
  4. Equal angles: divide the total.
Examples: 180−115 = 65° · 360−140−90 = 130°

📖 Continue Your Journey

✓ G1 2D Shapes✓ G2 Triangles✓ G3 Quadrilaterals✓ G4 Regular and Irregular Polygons✓ G5 Circles✓ G6 3D Shapes✓ G7 Nets✓ G8 Types of Angles✓ G9 Measuring and Drawing AnglesG10 Angles on a Line and at a PointG11 Angles in TrianglesG12 Angles in QuadrilateralsG13 Vertically Opposite AnglesG14 Parallel and Perpendicular LinesG15 SymmetryG16 Coordinates (First Quadrant)G17 Coordinates (Four Quadrants)G18 TranslationG19 ReflectionG20 Geometry Problem Solving
→
Next Lesson: G11 Angles in TrianglesThe angles inside always total 180°.
📄 Free printable: Download the Angles on a Line and at a Point cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Frequently asked questions

Why do angles on a straight line add to 180°?

A straight line is half a full turn, and a full turn is 360° — so the angles on one side of a line total 180°.

How do you find a missing angle around a point?

Add the angles you know and subtract from 360°: with 140° and 90° known, the missing angle is 360 − 230 = 130°.

What's the most common mistake?

Using the wrong total — 360° for a line or 180° for a point — or forgetting to subtract every known angle.

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