This study notes covers Worked Example 2: Regular Polygon Interior Angle 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 5 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 2: Regular Polygon Interior Angle
Find the size of each interior angle in a regular hexagon.
Method 1 Using interior angle formula
Each angle = (n − 2) × 180° ÷ n
= (6 − 2) × 180° ÷ 6
= 4 × 180° ÷ 6 = 720° ÷ 6 = 120°
Method 2 Using exterior angles (quicker!)
Exterior angle = 360° ÷ 6 = 60°
Interior + Exterior = 180°
Interior = 180° − 60° = 120°
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.