Worked Example 3: Finding Number of Sides

Part of Angles in Polygons · Section 6 of 10

Study NotesUnit: Geometry & MeasuresGCSE

A regular polygon has an exterior angle of 30°. How many sides does it have?

Step 1 Use the exterior angle formula

Exterior angle = 360° ÷ n

30° = 360° ÷ n

Step 2 Rearrange and solve

n = 360° ÷ 30°

n = 12 sides (dodecagon)

This study notes covers Worked Example 3: Finding Number of Sides within Angles in Polygons for GCSE Mathematics. Revise Angles in Polygons in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 10 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Practice questions for Angles in Polygons

What is the sum of the interior angles of a hexagon?

  • A. 540°
  • B. 720°
  • C. 900°
  • D. 360°
1 markfoundation

Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.

2 markshigher

Quick recall flashcards

Exterior Angle Sum
Always 360° for any polygon
Interior Angle Sum
Sum = (n - 2) × 180° for n-sided polygon

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Worked Example 2: Regular Polygon Interior Angle

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Worked Example 4: Missing Angle in Irregular Polygon

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