If an inner angle of a regular polygon is 108° , find the number of its sides.

إذا كان قياس الزاويه الداخلية لمضلع منتظم يساوي 108 فأوجد عدد اضلاعه  

A.

4

B.

5

C.

6

D.

7

To determine the number of sides in a regular polygon given its interior angle, we can use the formula for the interior angle of a regular polygon:

\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]

Where \( n \) is the number of sides.

Given that the interior angle is \( 108^\circ \), we can set up the equation:

\[
108^\circ = \frac{(n - 2) \times 180^\circ}{n}
\]

To solve for \( n \), multiply both sides by \( n \) to eliminate the fraction:

\[
108n = (n - 2) \times 180
\]

Now, distribute the \( 180 \) on the right side:

\[
108n = 180n - 360
\]

Next, move \( 108n \) to the right side:

\[
0 = 72n - 360
\]

Add \( 360 \) to both sides:

\[
360 = 72n
\]

Finally, divide by \( 72 \) to solve for \( n \):

\[
n = \frac{360}{72} = 5
\]

Thus, the number of sides in the polygon is \( 5 \), which corresponds to a **pentagon**.

The correct answer is **B. 5**.

Would you like more details or have any questions about this? 

Here are some related questions:

1. What is the formula for the exterior angle of a regular polygon?
2. How does the sum of the interior angles of a polygon relate to the number of sides?
3. What is the relationship between the number of sides and the number of diagonals in a polygon?
4. Can a polygon have an interior angle greater than 180°? Why or why not?
5. How can you calculate the area of a regular polygon?
6. What is the difference between a regular and an irregular polygon?
7. How does the side length affect the area of a regular polygon?
8. What are the properties of a polygon with 10 sides (decagon)?

**Tip:** The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360°.

Learn how to find the number of sides of a regular polygon given its interior angle of 108°. Step-by-step solution using the formula for the interior angle of a polygon. Suitable for students in Grades 7-9.

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