Question

The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.

Answer 1

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Here's the answer:

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¶¶¶ POINTS TO REMEMBER:

¶ The sum of the measures of the interior angles of a convex polygon with n sides  = $(n-2)×180^{\circ}$

• To find one Angle,(Measure of Single Exterior Angle)
The measure of any interior angle of a regular polygon with n sides = $\frac{n-2}{n}× 180^{\circ}$

¶ The sum of the measures of the exterior angles of polygon, one at each vertex, is $360^{\circ}$

• To find one Angle, (Measure of Single Exterior Angle)
The measure of any exterior angle of a regular polygon with n sides = $\frac{360^{\circ}}{n}$

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¶¶¶ SOLUTION :

Given,
The exterior angle of a regular polygon = $\frac{1}{3}$(its interior angle)

Let n be the number of sides of polygon

As per the question,
$\frac{360^{\circ}}{n} = \frac{1}{3}((n-2)×180^{\circ})$

$\implies \frac{n-2}{3} = 2$

$\implies n-2 = 6$

$\implies n = 8$

•°• The Number of Sides of polygon = $\underline{8}$

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