GCSE Maths Practice: polygons

Question 2 of 10

This question requires calculating the number of sides of a regular polygon given its interior angle.

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\( \begin{array}{l}\text{A regular polygon has an interior angle of } 162^\circ.\\ \text{How many sides does it have?}\end{array} \)

Choose one option:

Subtract the interior angle from 180° to get exterior angle; then 360° ÷ exterior angle = number of sides.

Regular polygons have equal sides and equal angles. The exterior angle can be calculated as 180° minus the interior angle. Once you have the exterior angle, divide 360° by it to get the number of sides. Here, interior angle = 162°, so exterior = 180 - 162 = 18°, giving 360 ÷ 18 = 20 sides. Understanding interior and exterior angle relationships is essential for solving problems involving polygons in GCSE geometry, helping with calculations, diagrams, and real-world applications such as tiling or design.