Any quadrilateral can be cut corner to corner into two triangles, so its four angles add up to 2 × 180 = 360°. Add the angles you know and take the total away from 360. Count a small square as 90°. When two angles have the same letter they are equal, so share what is left between them. The diagram is not drawn to scale.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- quadrilateral
- a flat shape with four straight sides
- diagonal
- a line joining opposite corners
Worked examples
A quadrilateral has angles 80°, 100°, 70° and ?. Find ?.
- 1.80 + 100 + 70 = 250.
- 2.360 − 250 = 110.
= 110
A quadrilateral has two right angles, a 115° angle and ?. Find ?.
- 1.90 + 90 + 115 = 295.
- 2.360 − 295 = 65.
= 65
A quadrilateral has angles 100°, 80° and two equal angles a. Find a.
- 1.360 − 180 = 180 for the two equal angles.
- 2.180 ÷ 2 = 90.
= 90
For parents
Method: Draw a diagonal on any four-sided shape to show the two triangles inside.
What to say: How many triangles fit inside a quadrilateral? So what do its angles add up to?
Common mistakes:
- Measures or estimates the angle from the picture instead of using an angle fact, although the diagram is not drawn to scale.
- Uses 180° (the triangle total) as the angle sum of a quadrilateral.
- Leaves out the angle marked with a small square because it has no number written on it.
- Subtracts only one of the labelled angles and forgets another.
- Finds what the equal unknown angles make together but does not share it between them.
- Adds the known angles and gives that total as the answer, without subtracting from the angle sum.