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Grade 8 / Parallel Lines and Angles 5 / 6

Sum of the Exterior Angles of a Polygon

For any polygon, the sum of the exterior angles is always 360°.

Example ①
Find one exterior angle of a regular hexagon.
Answer: Sum of exterior angles = 360°. One exterior angle of a regular hexagon = 360°÷6 = 60°
Example ②
What polygon has one exterior angle measuring 24°?
Answer: 360°÷24° = 15. Regular 15-gon.
Key Points
  • Sum of exterior angles = 360° (regardless of the type of polygon)
  • One exterior angle of a regular n-gon = 360°/n
  • Interior angle + exterior angle = 180° (at one vertex)

Practice Problems

  1. Find one exterior angle and one interior angle of a regular octagon.
  2. Of the five exterior angles of a pentagon, four are 55°, 65°, 70°, and 80°. Find the remaining exterior angle.

Answer and Explanation

  1. Answer: Exterior angle 45°, interior angle 135°. Exterior angle=360/8=45. Interior angle=180−45=135.
  2. Answer: 90°. 360−(55+65+70+80)=360−270=90.

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Sum of the Interior Angles of a Polygon
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Parallel Lines and Angles Test

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