Skip to main content
MathidiaMathematics Academy
Angle reasoning and constructions
Lesson 42 of 75
Easy practice

Angles in polygons

Objective. Calculate interior and exterior angles of polygons.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Angles in polygons follow fixed rules: the interior angles of any polygon with n sides sum to (n − 2) × 180°, while the exterior angles of any convex polygon always sum to 360°. For a regular polygon, dividing these totals by n gives each interior or exterior angle. A regular hexagon has 6 sides, so interior angles sum to (6 − 2) × 180° = 720°, giving each interior angle as 720° ÷ 6 = 120°. Always check whether the polygon is regular before dividing the total equally between its angles.

Worked example

Find the size of each interior angle of a regular polygon with 9 sides.

9
Illustrated card showing 9
  1. 1Find the interior angle sum: (9 − 2) × 180° = 1260°
  2. 2Divide by the number of sides since it's regular: 1260° ÷ 9
  3. 3Calculate: 1260 ÷ 9 = 140
  4. 4Each interior angle is 140°

Answer: 140°

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils often forget to subtract 2 from n before multiplying by 180°, calculating the interior angle sum of a hexagon as 6 × 180° = 1080° instead of 720°. Always use (n − 2) × 180° for the interior angle sum.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard