Geometry and proof · Ages 13–14

Exterior angles 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 exterior angle of a regular 6-sided polygon =
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2.Every side of the pentagon is extended, giving five exterior angles. x =
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3.Each exterior angle of a regular polygon is 60°. It has sides.
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4.Each exterior angle of a regular polygon is 90°. It has sides.
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5.Each angle of a regular polygon is 90°. Each exterior angle = °, and it has sides.
Fill in each blank
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6.Every side of the hexagon is extended, giving six exterior angles. x =
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7.Each angle of a regular polygon is 150°. Each exterior angle = °, and it has sides.
Fill in each blank
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8.Each angle of a regular polygon is 2 times each of its exterior angles. Each exterior angle = °, and it has sides.
Fill in each blank
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9.The picture marks one interior angle and four exterior angles of the pentagon. x =
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10.One side of the hexagon is extended. x =
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13.Each exterior angle of a regular polygon is 36°. What is each interior angle?
- A. 10°
- B. 36°
- C. 324°
- D. 144°
Choose the right answer
Working:
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14.A toy car drives once round a track shaped like a regular 8-sided polygon. At each corner it turns °, and back at the start it has turned ° in all.
Fill in each blank
Working:
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15.Each angle of a regular polygon is 120° more than each exterior angle. How many sides does it have?
Working:
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16.Each angle of a regular polygon is 108°. Find its number of sides n: put the steps in order.
- A. n × 72° = 360° (sum of ext. ∠s of polygon)
- B. each exterior angle = 180° − 108° = 72° (adj. ∠s on st. line)
- C. n = 360 ÷ 72 = 5
Write the letters in the right order
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17.A regular polygon's angles can each be 145°.
True or false?
Working:
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18.A toy car drives once round a track shaped like a regular 6-sided polygon. At each corner it turns °, and back at the start it has turned ° in all.
Fill in each blank
Working:
Answer:

Show the answers and working

Exterior angles of a polygon worksheet: Answers and working

1. 60°
The exterior angles add to 360° and all 6 are equal: each is 360° ÷ 6 = 60°.
2. 87°
A convex polygon's exterior angles add to 360° (sum of ext. ∠s of polygon): x = 360° − 273° = 87°.
3. 6
Sides = 360° ÷ one exterior angle = 360° ÷ 60° = 6.
4. 4
Sides = 360° ÷ one exterior angle = 360° ÷ 90° = 4.
5. 90, 4
Exterior = 180° − 90° = 90° (adj. ∠s on st. line), sides = 360° ÷ 90° = 4.
6. 38°
However many sides, the exterior angles add to 360° (sum of ext. ∠s of polygon): x = 360° − 322° = 38°.
7. 30, 12
Exterior = 180° − 150° = 30° (adj. ∠s on st. line), sides = 360° ÷ 30° = 12.
8. 60, 6
Interior + exterior = 180° (adj. ∠s on st. line), so 2 exterior angles and one more, 3 in all, make 180°: exterior = 180° ÷ 3 = 60°, and sides = 360° ÷ 60° = 6.
9. 73°
Turn the interior angle into an exterior one first: 180° − 105° = 75° (adj. ∠s on st. line). The exterior angles add to 360° (sum of ext. ∠s of polygon): x = 360° − 60° − 76° − 76° − 75° = 73°.
10. 64°
The sixth angle = 720° − 604° = 116° (∠ sum of polygon), so x = 180° − 116° = 64° (adj. ∠s on st. line).

11. False
The number of sides is 360° ÷ one exterior angle, and it must be whole: 360 ÷ 50 has to come out whole.
12. B. 360°
However many sides, a convex polygon's exterior angles add to 360° (sum of ext. ∠s of polygon).

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

13. D. 144°
Interior = 180° − 36° = 144° (adj. ∠s on st. line).
14. 45, 360
At each corner it turns through an exterior angle, 360° ÷ 8 = 45°; one lap is one full turn, 360° (sum of ext. ∠s of polygon).
15. 12
Interior + exterior = 180° and interior − exterior = 120°, so exterior = (180° − 120°) ÷ 2 = 30° and sides = 360° ÷ 30° = 12.
16. B → A → C
The exterior angle, 72°, from the interior one first; they add to 360°, so n = 360 ÷ 72 = 5.
17. False
Each exterior angle = 180° − 145° = 35°, and the sides = 360° ÷ 35°, which must be whole.
18. 60, 360
At each corner it turns through an exterior angle, 360° ÷ 6 = 60°; one lap is one full turn, 360° (sum of ext. ∠s of polygon).

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