Geometry and proof · Ages 13–14

Angle sum of a polygon worksheet

Part of: Polygons

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Geometry and proof · Ages 13–14

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

1.Each angle of a regular 6-sided polygon =
Answer:
2.The angles of a 7-sided polygon add up to
Answer:
3.The picture shows a pentagon. x =
Answer:
4.The angles of a 5-sided polygon add up to
Answer:
5.The diagonals from A cut the polygon into triangles, so its angles add up to × 180° = °.
Fill in each blank
Answer:
6.The picture shows a hexagon. x =
Answer:
7.The angles of a polygon add up to 1440°. It has sides.
Answer:
8.In the pentagon, the three angles marked x are equal. x =
Answer:
9.The angles of a polygon add up to 1080°. It has sides.
Answer:
10.The angles of a polygon add up to 1980°. It has sides.
Answer:

13.Four angles of a five-sided flower bed are 93°, 104°, 126° and 104°. The angles of a pentagon add to °, so the fifth = °.
Fill in each blank
Working:
Answer:
14.A polygon's angles can add up to 1350°.
True or false?
Working:
Answer:
15.A polygon's interior angles add to 4 times as much as its exterior angles. How many sides does it have?
Working:
Answer:
16.Four angles of a hexagon are 114°, 122°, 118° and 112°, and the other two are equal, x each. Find x: put the steps in order.
- A. 2x + 466° = 720°
- B. angle sum = (6 − 2) × 180° = 720°
- C. x = 127°
- D. 2x = 254°
Write the letters in the right order
Working:
Answer:
17.Someone works out a 6-sided polygon's angle sum as 6 × 180° = 1080°. What is it really?
- A. 1440°
- B. 720°
- C. 1080°
- D. 900°
Choose the right answer
Working:
Answer:
18.A polygon's angles can add up to 1710°.
True or false?
Working:
Answer:

Show the answers and working

Angle sum of a polygon worksheet: Answers and working

1. 120°
The angles add to (6 − 2) × 180° = 720°, and all 6 are equal: each is 720° ÷ 6 = 120°.
2. 900°
(n − 2) × 180° = (7 − 2) × 180° = 5 × 180° = 900° (∠ sum of polygon).
3. 83°
A pentagon's angles add to (5 − 2) × 180° = 540° (∠ sum of polygon): x = 540° − 457° = 83°.
4. 540°
(n − 2) × 180° = (5 − 2) × 180° = 3 × 180° = 540° (∠ sum of polygon).
5. 3, 3, 540
From one vertex a 5-sided polygon splits into 5 − 2 = 3 triangles, so its angles add to 3 × 180° = 540°.
6. 109°
A hexagon's angles add to (6 − 2) × 180° = 720° (∠ sum of polygon): x = 720° − 611° = 109°.
7. 10
(n − 2) × 180 = 1440, so n − 2 = 1440 ÷ 180 = 8 and n = 10.
8. 100°
3x + 101° + 139° = 540° (∠ sum of polygon), 3x = 300°, x = 100°.
9. 8
(n − 2) × 180 = 1080, so n − 2 = 1080 ÷ 180 = 6 and n = 8.
10. 13
(n − 2) × 180 = 1980, so n − 2 = 1980 ÷ 180 = 11 and n = 13.

11. D. 1440°
Angle sum = (n − 2) × 180° = (10 − 2) × 180° = 1440° (∠ sum of polygon).
12. D. 540°
Angle sum = (n − 2) × 180° = (5 − 2) × 180° = 540° (∠ sum of polygon).

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

13. 540, 113
Angle sum = (5 − 2) × 180° = 540° (∠ sum of polygon); the fifth = 540° − 93° − 104° − 126° − 104° = 113°.
14. False
The angle sum is (n − 2) × 180°, always a multiple of 180°: 1350 ÷ 180 must come out whole.
15. 10
The exterior angles make 360°, so the interior ones make 4 × 360° = 1440°: (n − 2) × 180 = 1440, n = 10.
16. B → A → D → C
The angle sum, 720°, first; then 2x + 466° = 720°, 2x = 254°, x = 127°.
17. B. 720°
The diagonals from one vertex make 6 − 2 triangles: (6 − 2) × 180° = 720° (∠ sum of polygon).
18. False
The angle sum is (n − 2) × 180°, always a multiple of 180°: 1710 ÷ 180 must come out whole.

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