Two regular polygons have the number of their sides in the ratio 1 : 2, and their interior angles in the ratio 3 : 4.
Find the number of sides of the smaller polygon.

Question

Two regular polygons have the number of their sides in the ratio 1 : 2, and their interior angles in the ratio 3 : 4. Find the number of sides of the smaller polygon.

Accepted Answer

5. Let sides be n and 2n. Interior angles are (n-2)180/n and (2n-2)180/2n = (n-1)180/n. Their ratio = n-2/n-1 = 3/4, so 4(n-2) = 3(n-1), 4n-8 = 3n-3, n = 5. Check: n=5 gives 108°, 2n=10 gives 144°, and 108:144 = 3:4. Smaller polygon has 5 sides.

Two regular polygons have the number of their sides in the ratio 1 : 2, and their interior angles in the ratio 3 : 4.
Find the number of sides of the smaller polygon.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Angle Sum of Polygons practice

Two regular polygons have the number of their sides in the ratio 1 : 2, and their interior angles in the ratio 3 : 4.Find the number of sides of the smaller polygon.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 8 Angle Sum of Polygons practice

Two regular polygons have the number of their sides in the ratio 1 : 2, and their interior angles in the ratio 3 : 4.
Find the number of sides of the smaller polygon.