Abdullah

**Solution:**

**Step:1** A regular polygon is defined as three or more sides having two-dimensional figure with equal magnitude of all interior angles and consequently all exterior angles.

Each interior angle of a regular polygon can be calculated by the formula , where *n* is the number of sides and formula is applicable for *n* greater than or equal to 3 sides.

**Step:2 **The formula is obtained by observing the pattern in three or more sided polygon sides and their sum of all interior angles.

The sum of all interior angles of the polygon is , where *n* is the number of sides and formula such that .

For regular polygon, each sides and each interior angles are equal.

**Step:3 **Therefore, the measure of each interior of *n-*sided regular polygon can be calculated by dividing the total sum of interior angles from total number of sides.

So, each interior angle of *n-*sided polygon is

**Step:4 **For example, each interior angle of a hexagon can be calculated by substituting in the above formula.

Therefore, each interior angle of a regular hexagon is equal to .

Simillarly, each interior angle of a regular quadrilateral can be calculated by substituting in the formula .

Therefore, each interior angle of a regular quadrilateral is equal to .

**Answer: **The Each interior angle of a regular polygon can be calculated by the formula , where *n* is the number of sides.

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**Similar Problems:**

**Problem 1: **Find the sum of interior angles of a pentagon.

**Solution:**

** **

**Step:1** The pentagon has five sides. It is a 5 sided polygon.

**Step:2 **The sum of all interior angles of the polygon is , where *n* is the number of sides and formula such that .

**Step:3 **Substitute in the formula and obtain the sum of interior angles of a pentagon.

Therefore, the sum of interior angles of a pentagon is 540 degree.

** **

**Answer:**

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The sum of interior angles of a pentagon is 540 degree.

**Problem 2:** Find each interior angles of a regualr pentagon.

**Solution:**

** **

**Step:1** The pentagon has five sides. It is a 5 sided polygon.

**Step:2 **Each interior angle of a regular polygon can be calculated by the formula , where *n* is the number of sides and formula is applicable for *n* greater than or equal to 3 sides.

**Step:3 **Substitute in the formula and obtain the each of interior angles of a regular pentagon.

Therefore, each interior angles of a regular pentagon is equal to .

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**Answer:**

** **

The each interior angles of a regular pentagon is equal to .

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