Question 42

If the measure of each exterior angle of a regular polygon is $$\left(51\frac{3}{7}\right)^\circ$$ then the ratio of the number of its diagonals to the number of its sides is:

Solution

Exterior angle of a regular polygon = 360/n

(where n = sides of polygon)

$$51\frac{3}{7} = 360/n$$

$$\frac{360}{7} = \frac{360}{n}$$

n = 7

Number of diagonal = $$\frac{n(n - 3)}{2} = \frac{7(7 - 3)}{2} = 14$$

The ratio of the number of its diagonals to the number of its sides = 14 : 7 = 2 : 1

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