Question

Two regular polygons X and Y are such that the number of sides of X is
3 more than the number of sides of Y. If the sum of the exterior angles
of X and Y is 117°, how many sides has .X?

Answer 1

Based on the indices of the regular polygons, the number of sides that X has is 8. See the computation below.

What is the analysis for the above solution?

Assuming that X has G number of sides; and

Y has H number of sides, this means that:

G-H = 3 ...........1

Recall that the formula for the exterior angles is:

360/n; where n is number of sides

X = 360/G

Y = 360/H

(360/G) + (360/H) = 117°.......2

Solving 1 and 2 simultaneously, we obtain:

G= 8 and

H = 5

Thus, X has 8 sides.

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