Question

The number of sides of two regular polygons are as 5:4 and the difference between their angles is 9°. Find the number of sides of the polygons,

Answer 1

Answer:

8 and 10.

Step-by-step explanation:

I am assuming the difference of 9° is between their interior angles.

The formula for the interior angle of a regular polygon is 180° - 360°/n, where n is the number of sides.

As the number of sides increase, the interior angle increases.

Therefore 180° - 360°/(5x) = 180° - 360°/(4x) + 9°.

180° - 360°/(5x) = 180° - 360°/(4x) + 9°

360°/(4x) = 360°/(5x) + 9°

90°/x = 72°/x + 9x°/x

=> 90° = 72° + 9x°

9x° = 18°

x = 2.

Hence the number of sides of the regular polygons are 8 and 10.