Question

Find the measure of each exterior angle of a regular (i) Heptagon (ii) polygon of 15 sides

Answer 1

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✴ Required Answer:

✏ GiveN:

• We have two regular polygons - 1) Heptagon and 2) A polygon with 15 sides.

✏ To FinD:

• Measure of each exterior angle....?

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✴ How to solve?

Before solving the question, let's know what is an exterior angle? and how to find the exterior angle of a regular polygon.

$\large{ \bold{ \underline{ \underline{ \blue{What \: is \: exterior \: angle?}}}}}$

If we extend any interior angle of any polygon, then the linear pair forming with the interior angle is the exterior angle of the polygon. Do you know?! The sum of all exterior angles of a n-sided polygon is 360°

$\large{ \bold{ \underline{ \underline{ \blue{How \: to \: find \: exterior \: angle?}}}}}$

The sum of all exterior angles of a polygon = 360°. Here, we have n sides of polygon and it is a regular polygon, then each exterior angle:

Exterior angle( n sided polygon ) = 360°/n

❇ By using this, we can solve the question.....!

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✴ Solution:

(1) We have,

• Sum of exterior angles = 360°
• No. of sides = 7 (heptagon)

Then, by relation

➙ Exterior angle = 360°/7

➙ Exterior angle = 51.43° (approx.)

(2) We have,

• Sum of exterior angles = 360°
• No. of sides = 15

Then, by relation

➙ Exterior angle = 360°/15

➙ Exterior angle = 24° (approx.)

$\large{ \therefore{ \underline{ \underline{ \rm{ \pink{Hence \: solved \: \dag}}}}}}$

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