The sum of the interior angles of a polygon is a given as 1080o. Find the number of the sides of the polygon.

Analysis

To find the number of sides of a polygon when the sum of its interior angles is known, we use the geometric formula relating the number of sides ($n$) to the sum of interior angles ($S$).

Concept

The formula for the sum of the interior angles of any polygon with $n$ sides is:

Where:

• $S$ is the sum of the interior angles.
• $n$ is the number of sides of the polygon.

Solution

Step 1: Set up the equation. Given that $S = 1080^\circ$, we substitute this into our formula:

Step 2: Isolate the term with $n$. Divide both sides of the equation by $180$:

Step 3: Perform the division.

Step 4: Solve for $n$. Add 2 to both sides:

The polygon has 8 sides (it is an octagon).

Conclusion

Comparing our result to the given options, the correct answer is D.

Exam Tip

A quick way to remember this is to divide the given sum by 180 first, then simply add 2 to the result. Also, remember that a triangle ($n=3$) has a sum of $180^\circ$, a quadrilateral ($n=4$) has $360^\circ$, and every time you add a side, you add another $180^\circ$ to the total sum!