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Geometry & MeasuresStudy Notes

Worked Example 3: Finding Number of Sides

Part of Angles in Polygons — GCSE Mathematics

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 9 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 9

Practice

12 questions

Recall

3 flashcards

Worked Example 3: Finding Number of Sides

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)

Keep building this topic

Read this section alongside the surrounding pages in Angles in Polygons. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 2: Regular Polygon Interior AngleWorked Example 4: Missing Angle in Irregular PolygonThe Triangle TrickEssential Formulas

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