If the ratio of the number of diagonals to number of interior angles in a polygon is 7, then the number of sides of the polygon is:

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Solution

The correct option is A
17

The number of diagonals in a polygon = $\frac{n (n - 3)}{2}$ .
Number of interior angles = n.
Thus, the ratio of number of diagonals to number of interior angles in a polygon = $\frac{n (n - 3)}{2 n} = 7$ .
n -3 =14
n =17
The number of sides of the polygon is 17.

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If the ratio of the number of diagonals to number of interior angles in a polygon is 7, then the number of sides of the polygon is:

The correct option is A 17 The number of diagonals in a polygon = n(n−3)2. Number of interior angles = n. Thus, the ratio of number of diagonals to number of interior angles in a polygon = n(n−3)2n=7. n -3 =14 n =17 The number of sides of the polygon is 17.

The correct option is A
17

The number of diagonals in a polygon = $\frac{n (n - 3)}{2}$ .
Number of interior angles = n.
Thus, the ratio of number of diagonals to number of interior angles in a polygon = $\frac{n (n - 3)}{2 n} = 7$ .
n -3 =14
n =17
The number of sides of the polygon is 17.