Question A polygon has an interior angle that is five times larger than its exterior angle. How many sides does the polygon have?

Given the measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Each interior angle of a regular polygon =180°(n-2)/n Each exterior angle of a regular polygon = 360°/n According to question, 180°(n-2)/n = 5 × 360°/n 36(n-2) = 360 n-2=10 n=12 Number of sides of the polygon =12 Reply

Answer: The polygon has 12 sides —————————————————- We know the sum of a pair of interior and exterior angles is 180°. Let the exterior angle be x then we have: x + 5x = 180 6x = 180 x = 30 We also know that sum of all exterior angles is 360°. If the number of sides is n, then we have: 30n = 360 n = 360/30 n = 12 Reply

5=12Answer:sum of a pair of interior and exterior angles is 180°.exterior angle be xthen we have:x = 30sum of all exterior angles is 360°.number of sides is n, then we have:n = 12