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

Angles in Quadrilaterals

Draw one diagonal and any quadrilateral becomes two triangles — which is exactly why its angles total 360°. This lesson applies the subtract-from-360 routine and the parallelogram shortcuts.

G12Angles in Quadrilaterals
The four angles inside total 360°.
Every quadrilateral's angles add up to 360° — twice the triangle total.
Split any quadrilateral into two triangles.
2 triangles × 180° = 360°
Missing angle = 360° − the three you know.
1

Learn the 3-Step Method

1Know the total: 360°.

A diagonal splits any quadrilateral into two triangles: 2 × 180° = 360°.

360°

2Add the known angles.

90 + 85 + 100 = 275.

90+85+100 = 275

3Subtract from 360.

360 − 275 = 85. The missing angle is 85°.

360 − 275 = 85
💡 Key IdeaSpecial cases carry free information: rectangles have four 90°s; a parallelogram's opposite angles are equal.
2

Worked Example

A parallelogram has one angle of 110°. Find the other three.

Opposite angle
Opposite angles are equal
110°
→
Neighbouring pair
360 − 220 = 140
140 ÷ 2 = 70
→
✓ Answer
110°, 70°, 110°, 70°
Total: 360 ✓
3

Watch Out! Common Mistakes

✕
Using the triangle total.
quadrilateral: 180 − … ✕

Wrong total! Four sides → 360°. (Two triangles’ worth.)

✕
Missing one of the three knowns.
360 − 90 − 85 = 185° ✕

Subtract all three! 360 − 90 − 85 − 100 = 85°.

✕
Assuming every quadrilateral has a right angle.

Only some! Squares and rectangles have 90° corners; parallelograms, rhombuses and general quadrilaterals usually don’t.

⬇ Cheat Sheet

ANGLES IN QUADRILATERALS
  1. Quadrilateral angles always total 360°.
  2. Missing angle = 360 − the known three.
  3. Parallelogram: opposite angles equal; neighbours total 180°.
  4. Rectangle/square: all four are 90°.
Example: 360 − 90 − 85 − 100 = 85°

📖 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 Angles✓ G10 Angles on a Line and at a Point✓ G11 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: G13 Vertically Opposite AnglesX marks two pairs of equal angles.
📄 Free printable: Download the Angles in Quadrilaterals cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Frequently asked questions

Why do quadrilateral angles add to 360°?

A diagonal splits any quadrilateral into two triangles, each contributing 180° — so 360° in total.

How do you find a missing angle in a quadrilateral?

Add the three known angles and subtract from 360°: 360 − (90 + 85 + 100) = 85°.

What are the parallelogram angle rules?

Opposite angles are equal, and angles next to each other add up to 180° — so one angle of 110° forces the pattern 110°, 70°, 110°, 70°.

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