Maths · Geometry & Measures
Angle rules
Angles on a line, at a point, and in triangles.
Angles on a Straight Line
When angles sit on a straight line, they always add up to 180°. This is because a straight line forms a half-turn. If you know some angles, subtract them from 180° to find the missing one.
Angles Around a Point
Angles that meet at a point add up to 360°. A full turn is 360°, so all angles around any point must total this amount. This rule helps us find unknown angles quickly.
Angles in a Triangle
The three interior angles (inside angles) of any triangle always add up to 180°. It doesn't matter what shape the triangle is. Add the two known angles, then subtract from 180° to find the third.
Using Angle Rules Together
Sometimes you need to use more than one rule to solve a problem. Look carefully at the diagram to spot which angles are on a line, around a point, or inside a triangle.
Worked examples
1. Two angles on a straight line are 110° and x°. Find x.
- Angles on a straight line add up to 180°.
- So 110° + x° = 180°.
- Subtract 110° from both sides: x = 180° - 110° = 70°.
2. A triangle has angles 50°, 65° and y°. Find y.
- Angles in a triangle add up to 180°.
- So 50° + 65° + y° = 180°.
- Add the known angles: 50° + 65° = 115°.
- Subtract from 180°: y = 180° - 115° = 65°.
3. Three angles around a point are 140°, 85° and z°. Find z.
- Angles around a point add up to 360°.
- So 140° + 85° + z° = 360°.
- Add the known angles: 140° + 85° = 225°.
- Subtract from 360°: z = 360° - 225° = 135°.
Try it yourself
Two angles on a straight line are 92° and p°. Find p.
Ready to test yourself?
Take a short topic test — every question maps to a syllabus point so you’ll see exactly which parts you’ve mastered.