Question

1. what is the formula to calculate the sum of interior angles of a polygon?

a. ( s = n\times90^{circ} )
b. ( s = n\times180^{circ} )
c. ( s=(n - 2)\times180^{circ} )
d. ( s=(n + 2)\times90^{circ} )

Explanation:

Step1: Recall polygon interior - angle sum concept

For a triangle (\(n = 3\)), the sum of interior angles is \(180^{\circ}\). Substituting \(n=3\) into \(S=(n - 2)\times180^{\circ}\), we get \(S=(3 - 2)\times180^{\circ}=180^{\circ}\).

Step2: Check for a quadrilateral (\(n = 4\))

A quadrilateral can be divided into two triangles. The sum of interior angles of a quadrilateral is \(360^{\circ}\). Substituting \(n = 4\) into \(S=(n - 2)\times180^{\circ}\), we have \(S=(4 - 2)\times180^{\circ}=2\times180^{\circ}=360^{\circ}\).
In general, a polygon with \(n\) sides can be divided into \((n - 2)\) non - overlapping triangles. Since the sum of interior angles of a triangle is \(180^{\circ}\), the sum of interior angles of an \(n\) - sided polygon \(S=(n - 2)\times180^{\circ}\).

Answer:

C. \( S=(n - 2)\times180^{\circ} \)