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Learn · Numeracy · 5 min

Angles: the four facts

Almost every angle question in an exam is one of four facts plus a subtraction. Learn the four and you can find a missing angle in any diagram:

See it: the angles at a point always add to the whole turn

130°50°

130° + 50° = 180°

Move it anywhere you like — the two always total 180°. That is the whole trick.

See it: a triangle’s three angles always total 180°

70°55°55°

70° + 55° = 125°  →  third angle = 180° − 125° = 55°

Now — the one move

Every missing-angle question is the same two steps. Name the fact, then subtract.

Worked example

  • Three angles sit on a straight line: 55°, x, and 70°.
  • ① Which fact? They’re on a straight line → they total 180°
  • ② Add what you know: 55° + 70° = 125°
  • ③ Subtract: x = 180° − 125° = 55°
  • Check: 55 + 55 + 70 = 180 ✓

Tips & tricks

Isosceles triangle — two angles are equal
Apex 40°, so the two base angles share 180 − 40 = 140 → each is 70°.
Equilateral triangle — all three are 60°
180 ÷ 3 = 60°, every time. Worth memorising.
Right angle in a triangle? The other two total 90°
One is 90°, so the rest share 180 − 90 = 90°.
Opposite angles at a crossing are equal
Two straight lines crossing make two pairs of equal (vertically opposite) angles.
Sanity-check the size
An angle that looks smaller than a square corner must come out under 90°. If your answer says 130°, you’ve used the wrong fact.

Now you try — 0/4

1. Two angles sit on a straight line. One is 145°. What is the other?

2. A triangle has angles of 40° and 55°. What is the third angle?

3. Four angles meet around a point: 90°, 80°, 80° and y. What is y?

4. An isosceles triangle has an apex angle of 30°. What is each base angle?

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