The idea, step by step
A full turn
Angles meeting at a point add to 360° when they fill one complete turn without overlapping. Start at one arm and move all the way around until you return to it.
Add the given angles, then subtract from 360°. Check that every part has been counted once. A straight-line total of 180° is not enough for a complete turn.
Equal unknown parts
Sometimes the remaining turn is divided into equal angles. First find the total space left after the known parts. Then share that remaining amount equally.
If one angle is 80° and the other two are equal, the remaining space is 280°. Each equal angle is 140°. This works because 80° + 140° + 140° = 360°.
A common trap
Using 180° for every missing-angle question.
Instead: Decide which whole is shown: a straight half-turn is 180°, but a full turn around a point is 360°.
See the thinking
One missing sector
Three angles around a point are 70°, 120° and x. Find x.
- 70° + 120° = 190°.
- 360° − 190° = 170°.
Four parts
Four angles fill a full turn. Three are 90°, 85° and 110°. Find the fourth.
- Known total: 90° + 85° + 110° = 285°.
- 360° − 285° = 75°.
Check your understanding
Angles around a point are 100°, 150° and x. Find x.
Show answer
110°
100 + 150 = 250, then 360 − 250 = 110.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Three angles around a point are 90°, 130° and x. Find x.2 marks
- Four angles around a point are 65°, 95°, 110° and x. Find x.2 marks
- One angle is 120°. The other two angles around the point are equal. Find each equal angle.2 marks
- Six equal angles fill a full turn. Find each angle.1 mark
- Mia lists angles of 90°, 90°, 80° and 90° for one complete turn. What is wrong?2 marks
- Three angles around a point are 75°, 140° and x. Draw a rough sketch, find x and check the total.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Three angles around a point are 90°, 130° and x. Find x.2 marks
360° − (90° + 130°) = 140°.
140° - Four angles around a point are 65°, 95°, 110° and x. Find x.2 marks
65 + 95 + 110 = 270.
360 − 270 = 90.
90° - One angle is 120°. The other two angles around the point are equal. Find each equal angle.2 marks
360° − 120° = 240°.
240° ÷ 2 = 120°.
120° - Six equal angles fill a full turn. Find each angle.1 mark
360° ÷ 6 = 60°.
60° - Mia lists angles of 90°, 90°, 80° and 90° for one complete turn. What is wrong?2 marks
90 + 90 + 80 + 90 = 350.
A full turn is 360°, leaving a 10° gap.
They total 350°, so 10° is missing. - Three angles around a point are 75°, 140° and x. Draw a rough sketch, find x and check the total.3 marks
75° + 140° = 215°.
360° − 215° = 145°.
75° + 140° + 145° = 360°.
x = 145°
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 6 angle relationships: straight-line angles, angles around a point, vertically opposite angles and connected reasoning.
Official curriculum source ↗