Question

The measure of each exterior angle of regular polygon is 60°. Find the no. Of the sides of the polygon and hense the measure of each exterior angle

Answer 1

Correct Question: The measure of each exterior angle of regular polygon is 60°. Find the no. Of the sides of the polygon and hence the measure of each interior angle.

Solution:

Number of sides of polygon (when exterior angle is given) is calculated by the  formula:

→ n = 360° ÷ x

Where, 'x' refers to the measure of exterior angle and 'n' refers to the number of sides of the polygon.

According to the question, x = 60°. Therefore 'n' is calculated as:

→ n = 360° ÷ 60°

→ n = 6

Therefore the given polygon is a 6 sided polygon. (Hexagon)

Sum of Interior angles is given by the formula:

→ ( n - 2 ) × 180°

Where, 'n' refers to the number of sides of a polygon.

Substituting n = 6, we get:

→ Sum of Interior angle = ( 6 - 2 ) × 180°

→ Sum of Interior angle = 4 × 180° = 720°

Now 6 sides have a sum of 720°. Therefore one side would have:

→ 720° ÷ 6 = 120°

Hence the measure of each interior angle is 120°

Answer 2

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Given :

• Angle is 60°

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To Find :

• Measure of each exterior angle

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Solution :

We have formula for Number of Sides

$\large \star {\boxed{\sf{No. \: of \: Sides \: = \dfrac{360}{Given \: Angle}}}} \\ \\ \implies {\sf{No. \: of \: Sides \: = \: 6}}$

No. of Sides of Polygon is 6

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And formula for Sum of internal angles is :

$\large \star {\boxed{\sf{Sum \: = \: (No. \: of \: Sides \: - \: 2) \: \times \: 180}}} \\ \\ \implies {\sf{Sum \: = \: (6 \: - \: 2) \: \times \: 180}} \\ \\ \implies {\sf{Sum \: = \: 4 \: \times \: 180}} \\ \\ \implies {\sf{Sum \: = \: 720}}$

Sum of Internal Angles is 720°

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⇒Each Angle = 720/6

⇒Each angle = 120°

Each angle is of 120°