Year 8 · Maths · Angles in polygons · Lesson 2
Interior angles of polygons
Find the sum of interior angles of any polygon, missing angles, interior angles of regular polygons and the number of sides from the angle sum.
30-minute video lesson
Teaching, worked examples and 20 practice questions solved step by step.
Watch free for a monthWhat your child will learn
- Name polygons
- Find the sum of interior angles
- Find missing interior angles
- Find each interior angle of a regular polygon
- Find the number of sides from the angle sum
The method
- Sum of interior angles = (number of sides − 2) × 180°.
- Missing angle: sum minus the others.
- Regular polygon: each angle = sum ÷ number of sides.
- Number of sides = sum ÷ 180 + 2.
Key words: polygon, interior angle, regular, sum, triangle.
Worked examples
The first three practice questions from the lesson, with every step.
Question 1
Find the sum of the interior angles of a quadrilateral.
- Step 1: 4 sides
- Step 2: 4 − 2 = 2 triangles
- Step 3: 2 × 180° = 360°
Answer: 360°
Question 2
Find the sum of the interior angles of a hexagon.
- Step 1: 6 sides
- Step 2: 6 − 2 = 4 triangles
- Step 3: 4 × 180° = 720°
Answer: 720°
Question 3
Find the sum of the interior angles of a heptagon.
- Step 1: 7 sides
- Step 2: 7 − 2 = 5 triangles
- Step 3: 5 × 180° = 900°
Answer: 900°