The three angles inside any triangle add up to 180°. If you tear off the corners of a paper triangle, they fit together on a straight line. To find a missing angle, add the two you know and take the total from 180. A small square means 90°. In an isosceles triangle, two sides are equal, so the two angles at the ends of the third side are equal too.
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
- angle sum
- what all the angles in a shape add up to
- isosceles
- a triangle with two equal sides and two equal angles
Worked examples
A triangle has angles 50°, 65° and ?. Find ?.
- 1.Add the angles you know: 50 + 65 = 115.
- 2.180 − 115 = 65.
= 65
A right-angled triangle has a 35° angle. Find the third angle.
- 1.The right angle is 90°: 90 + 35 = 125.
- 2.180 − 125 = 55.
= 55
An isosceles triangle has a 40° angle at the top and two equal angles a. Find a.
- 1.180 − 40 = 140 for the two equal angles.
- 2.140 ÷ 2 = 70.
= 70
For parents
Method: Tear the corners off a paper triangle and line them up on a straight edge.
What to say: What do the angles in a triangle add up to? Which angles do you know already?
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 360° as the total instead of 180°.
- Leaves out the angle marked with a small square because it has no number written on it.
- In an isosceles triangle, uses the one labelled base angle but forgets the equal base angle shown by the side marks.
- 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.