Angles in polygons
Maths, Geometry. Usually met in years 7 to 10.
Work out missing angles in triangles, round a point and in polygons, using angle sums and exterior angles.
What you practise
- Angles in a triangle and round a point
- Sum of the interior angles of a polygon
- Interior and exterior angles of regular polygons
Ends with working out the number of sides from an angle. Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
Three angles round a point are 56°, 84° and 62°. What is the fourth angle?
- 158°
- 148°
- 168°
- 202°
- 220°
Show the answer and method
Answer: A, 158°
The method: Angles round a point add to 360°. 56 + 84 + 62 = 202, so the fourth angle is 360 − 202 = 158°.
Why the other options are wrong:
- B, 148°: Close, but check your working: this is a small slip away from the answer.
- C, 168°: Close, but check your working: this is a small slip away from the answer.
- D, 202°: This is the total of the three angles.
- E, 220°: One of the angles was forgotten.
Sample question, level 4 of 5
What is the size of each interior angle of a regular polygon with 9 sides?
- 1260°
- 140°
- 40°
- 150°
- 20°
Show the answer and method
Answer: B, 140°
The method: The interior angles add up to (9 − 2) × 180 = 1260°. All 9 angles are equal: 1260 ÷ 9 = 140°.
Why the other options are wrong:
- A, 1260°: This is the sum of all the interior angles, not one angle.
- C, 40°: This is the exterior angle, not the interior angle.
- D, 150°: Check the subtraction.
- E, 20°: The angle sum was not worked out first.
See where this fits: GCSE maths with AQA and Key Stage 3.
Related topics: Pythagoras, Area of a circle.
