Question

if the sum of interior angles of a polygon is $900^{circ}$, how many sides does the polygon have?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \), where \( S \) is the sum of the interior angles and \( n \) is the number of sides.

Step2: Substitute the given sum into the formula and solve for \( n \)

We know that \( S = 900^{\circ} \). Substituting this into the formula \( (n - 2)\times180^{\circ}=900^{\circ} \).
First, divide both sides of the equation by \( 180^{\circ} \):
\( n - 2=\frac{900^{\circ}}{180^{\circ}} \)
\( n - 2 = 5 \)
Then, add 2 to both sides of the equation:
\( n=5 + 2 \)
\( n = 7 \)

Answer:

The polygon has 7 sides.