GCSE Maths Practice: polygons

Question 1 of 10

This question asks students to find the number of sides in a regular polygon given its interior angle.

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\( \begin{array}{l}\text{A regular polygon has interior angles of } 135^\circ.\\ \text{How many sides does it have?}\end{array} \)

Choose one option:

Use formula: Exterior angle = 180° - interior angle; then 360° ÷ exterior angle = number of sides.

Regular polygons have all sides equal and all angles equal. The exterior angle is the difference between 180° and the interior angle. Once you know the exterior angle, divide 360° by this value to find the number of sides. Here, interior angle = 135°, so exterior angle = 180° - 135° = 45°. Then 360° ÷ 45° = 8 sides. Understanding the relationship between interior and exterior angles is crucial for solving problems with polygons, diagrams, and geometric proofs at GCSE. Practising these calculations improves recognition of polygon properties and helps with reasoning about angles and shapes.