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.
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)
Practice questions for Angles in Polygons
What is the sum of the interior angles of a hexagon?
Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.