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Sum of Angles of n-sided Polygon

The sum of the angles of an n-sided polygon is (n - 2) × 180°; where n is equal to the number of sides of the polygon.

Example: A pentagon is a 5-sided polygon, and the sum of its angles is equal to (5-2)×180°. 5 - 2 = 3 and 3 × 180° = 540°, which means that the sum of the angles of a pentagon is equal to 540°.

In harmony, a standard pentagon is a regular pentagon. The beauty about a regular pentagon is that all its sides are of equal magnitude. After all, the harmonious world is about equality and balance.

Since there are five angles in a pentagon, each angle of a regular pentagon is equal to the sum of the angles of a regular pentagon divided by the number of sides of the pentagon.

Let the sum of the angles of the regular pentagon be S, the number of sides n and each angle A.


A = S/n

Since S = 540°,
n = 5 and
A = 540°/5
   = 108°

Question 1:
what is the sum of the angles of a regular hexagon?

A hexagon is a 6-sided polygon, which means that n = 6.

Sum of angles of a polygon = (n - 2) × 180°.

Sum of angles of a regular hexagon = (6 - 2) × 180°

= 4 × 180°
= 720°

Question 2:
What is the magnitude of each angle of a regular octagon?

An octagon is an 8-sided polygon, which means that n = 8.

S (Sum of the angles of a polygon) = (n - 2) × 180°.

Substituting 8 for n,
S = (n - 2) × 180°
   = 1080°

A (an angle) = S/n
                       = 1080°/8
                       = 135°



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Qibla compass is designed specifically to help Muslims locate the direction of Mecca and pray facing the Kaaba. Some designs have the word "Mecca" inscribed as the most prominent direction on the compass; others have the image of the Kaaba or a Mosque signifying the qibla (Muslim direction) on the compass.
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