Angles · Usually met around P6
Angles of regular polygons
Angle sum = (sides − 2) × 180°, then ÷ sides.
How to do it
Method
Angle sum = (sides − 2) × 180°, then ÷ sides
Regular hexagon: (6 − 2) × 180 = 720, 720 ÷ 6 = 120°
Another way
Walk round the edge
360 ÷ 6 = 60; 180 − 60 = 120
In full
A regular polygon has all its sides equal and all its angles equal. Draw every diagonal from one corner and a polygon with n sides splits into (n − 2) triangles, each with angles making 180°, so its angles add up to (n − 2) × 180°. Each angle of a regular n-sided polygon = that sum ÷ n: a regular hexagon has (6 − 2) × 180 = 720, and 720 ÷ 6 = 120°. Another way: walk once round the polygon's edge, turning the same amount at each corner, 360° in all: a hexagon turns 360 ÷ 6 = 60° at each corner, so each angle inside is 180 − 60 = 120°. Careful: 360 ÷ 6 = 60 is the turn, not the angle inside.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Every diagonal (dashed) is drawn from one corner of the regular polygon. How many triangles is it cut into?
Show the answer and working
Answer: 6
8 sides: from one corner it splits into 8 − 2 = 6 triangles.
Example 2
The picture shows a regular polygon. Its angles add up to □°, and each is □°.
Fill in each box
Show the answer and working
Answer: 1800，150
Count the sides: 12. The sum is (12 − 2) × 180 = 1800; each angle 1800 ÷ 12 = 150.
Example 3
Each angle of a regular polygon with 5 sides is 72°.
True or false?
Show the answer and working
Answer: False
Each angle = (5 − 2) × 180 ÷ 5 = 108°.
Practise it in the game →Angles · Free to start, unlimited questions, no download