If the ratio between the interior and exterior angles of a regular polygon is 14 : 1, then the polygon has ___ sides.

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Solution

The correct option is D
30

Let the interior angle (i) = 14x and the exterior angle (e) = x

We know, i + e = $180^{\circ}$

14x + x = $180^{\circ}$

15x = $180^{\circ}$

x = $12^{\circ}$

$∴ e = 12^{\circ}$

$n = \frac{360^{\circ}}{e^{\circ}}$

$\frac{360^{\circ}}{12^{\circ}}$

= 30

Ans (D)

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If the ratio between the interior and exterior angles of a regular polygon is 14 : 1, then the polygon has ___ sides.

The correct option is D 30 Let the interior angle (i) = 14x and the exterior angle (e) = x We know, i + e = 180∘ 14x + x = 180∘ 15x = 180∘ x = 12∘ ∴ e=12∘ n=360∘e∘ 360∘12∘ = 30 Ans (D)

The correct option is D
30

Let the interior angle (i) = 14x and the exterior angle (e) = x

We know, i + e = $180^{\circ}$

14x + x = $180^{\circ}$

15x = $180^{\circ}$

x = $12^{\circ}$

$∴ e = 12^{\circ}$

$n = \frac{360^{\circ}}{e^{\circ}}$

$\frac{360^{\circ}}{12^{\circ}}$

= 30

Ans (D)