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Angles in a Triangle

In one line: The three angles inside any flat triangle always add up to exactly 180 degrees, so if you know two of them, you can work out the third.

Why it works

An angle measures how much two lines turn away from each other where they meet, and we measure it in degrees (°). Knowing that a triangle's inside angles always total 180° lets you find a missing angle without a protractor, which is a tool for measuring angles. This rule is used everywhere in geometry, from solving puzzles about shapes to working out angles in roofs, bridges and maps. It is also the stepping stone to bigger ideas, like the angles in a four-sided shape adding to 360°.

Think of it like: Think of a triangle as three friends sharing exactly 180 sweets. However the sweets are split, the total is always 180, so if one friend takes more, the other two must end up with fewer. If you know how many two friends have, you can always work out what the third friend got by taking their share away from 180. (Where this breaks: The analogy breaks because a friend could get zero sweets, but a triangle's angle can never be 0°: each angle must be more than 0°, or the shape would flatten into a line. Also, the 180° rule only works on flat surfaces like paper; a triangle drawn on a curved surface, such as a ball, has angles that add up to more than 180°.)

Worked example

A triangle has two angles of 47° and 68°. What is the size of the third angle?

  1. Remember the rule: the three angles inside a triangle add up to 180°.
  2. Add the two angles you know: 47° + 68° = 115°.
  3. Take that total away from 180°: 180° − 115° = 65°.
  4. Check your answer by adding all three: 47° + 68° + 65° = 180°. It works.

Answer: The third angle is 65°.

Common mistakes

  • Subtracting from 360° instead of 180° mixes up triangles with full turns or four-sided shapes, so always start from 180° for a triangle.
  • Forgetting that a small square in a corner marks a right angle (exactly 90°) leaves out an angle, so count that 90° in your total.
  • Halving the wrong angle in an isosceles triangle (a triangle with two equal sides and two equal angles) gives a wrong answer, so check which two angles sit opposite the equal sides.
  • Rushing the subtraction, such as 180 − 115 = 75, causes errors, so always add all three angles at the end to check they make 180°.

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A triangle has angles of 60° and 70°. What is the third angle?

Questions parents ask

What year do kids learn about angles in a triangle?

In the UK, children usually learn that triangle angles add to 180° in Year 6, building on angle work from Years 4 and 5. In Australia it is a focus in Year 7, and in the US it is typically covered around Grades 7 to 8, though many children meet it earlier.

How can I help my child with angles in a triangle at home?

Cut out a paper triangle, tear off its three corners and line them up point to point: they form a straight line, which is 180°. Then make up quick missing-angle puzzles and ask your child to check each answer by adding all three angles.

Why do the angles in a triangle add up to 180°?

If you draw a line through one corner of a triangle, parallel to (running alongside and never meeting) the opposite side, the three angles fit together along that straight line. A straight line is always 180°, so the three angles must total 180° too.

Does the 180° rule work for every triangle?

Yes, it works for every triangle drawn on a flat surface, whether it is tall and thin, right-angled or has all sides equal. The only exception is triangles drawn on curved surfaces like a globe, which children usually meet much later.