Shape and space · Ages 11–12

Angles of regular polygons worksheet

Part of: Angles

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Shape and space · Ages 11–12

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Every diagonal (dashed) is drawn from one corner of the regular polygon. How many triangles is it cut into?
Answer:
2.What do the angles of a regular polygon with 8 sides add up to, in degrees?
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3.The picture shows a regular polygon. What is the angle marked ? in degrees?
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4.The picture shows a regular polygon. Its angles add up to °, and each is °.
Fill in each blank
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5.Each angle of a regular polygon is 135°. How many sides does it have?
Answer:
6.Each angle of a regular polygon is 162°. How many sides does it have?
Answer:

13.Three tiles meet at a point with no gap. One is a regular polygon with 10 sides and one has 8 sides. How many degrees is the third tile's angle at that point?
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14.May makes a regular polygon-shaped flower bed from 6 bamboo poles of the same length. How many degrees is each angle of the bed?
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15.A flower bed is a regular polygon whose angles are each 144°. How many sides does it have?
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16.Chi-keung walks once round the edge of a regular flower bed with 5 sides, turning at every corner. How many degrees is each turn?
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17.A flower bed is a regular polygon whose angles are each 120°. How many sides does it have?
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18.Ka-lok makes a regular polygon-shaped flower bed from 9 bamboo poles of the same length. How many degrees is each angle of the bed?
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Show the answers and working

Angles of regular polygons worksheet: Answers and working

1. 2
Count the pieces the dashed lines make, or think how the number of triangles relates to the number of sides.
4 sides: from one corner it splits into 4 − 2 = 2 triangles.
2. 1080°
Drawing diagonals from one corner, how many triangles does a shape with 8 sides split into? Each triangle is 180°.
It splits into 8 − 2 = 6 triangles: 6 × 180 = 1080.
3. 144°
Count the sides first, then find the angle sum with (sides − 2) × 180°.
Count the sides: 10. The angles add to (10 − 2) × 180 = 1440, each 1440 ÷ 10 = 144.
4. 1260, 140
Count the sides first, then think how many triangles the diagonals from one corner make.
Count the sides: 9. The sum is (9 − 2) × 180 = 1260; each angle 1260 ÷ 9 = 140.
5. 8
How far do you turn at each corner? Work out 180 − 135 first. A whole round is 360°.
Each corner turns 180 − 135 = 45°, and a whole round is 360°: 360 ÷ 45 = 8.
6. 20
How far do you turn at each corner? Work out 180 − 162 first. A whole round is 360°.
Each corner turns 180 − 162 = 18°, and a whole round is 360°: 360 ÷ 18 = 20.

7. True
Find the angle sum of the polygon with 8 sides, share it among the angles, and compare with 135.
Each angle = (8 − 2) × 180 ÷ 8 = 135°.
8. A. 36°
A whole walk round turns how many degrees? The 10 corners share that equally.
A whole walk round turns 360°, shared by 10 corners: 360 ÷ 10 = 36.
9. B. 40°
A whole walk round turns how many degrees? The 9 corners share that equally.
A whole walk round turns 360°, shared by 9 corners: 360 ÷ 9 = 40.
10. True
Find the angle sum of the polygon with 9 sides, share it among the angles, and compare with 140.
Each angle = (9 − 2) × 180 ÷ 9 = 140°.
11. C. 72°
A whole walk round turns how many degrees? The 5 corners share that equally.
A whole walk round turns 360°, shared by 5 corners: 360 ÷ 5 = 72.
12. False
Find the angle sum of the polygon with 5 sides, share it among the angles, and compare with 540.
Each angle = (5 − 2) × 180 ÷ 5 = 108°.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 81°
Find each angle of the 10-sided and 8-sided tiles first; round a point is 360°.
The 10-sided one's angle is 144° and the 8-sided one's 135°; round a point is 360°: 360 − 144 − 135 = 81.
14. 120°
6 poles make 6 sides. Find the angle sum first: (6 − 2) × 180°.
6 poles are 6 sides: the angles add to (6 − 2) × 180 = 720, each 720 ÷ 6 = 120.
15. 10 sides
How far do you turn at each corner? Work out 180 − 144 first. A whole round is 360°.
Each corner turns 180 − 144 = 36°, and a whole round is 360°: 360 ÷ 36 = 10.
16. 72°
How many degrees does one whole walk round turn? The 5 corners share it.
A whole walk round turns 360°, shared by 5 corners: 360 ÷ 5 = 72.
17. 6 sides
How far do you turn at each corner? Work out 180 − 120 first. A whole round is 360°.
Each corner turns 180 − 120 = 60°, and a whole round is 360°: 360 ÷ 60 = 6.
18. 140°
9 poles make 9 sides. Find the angle sum first: (9 − 2) × 180°.
9 poles are 9 sides: the angles add to (9 − 2) × 180 = 1260, each 1260 ÷ 9 = 140.

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