Question

what is the formula to calculate the sum of interior angles of a polygon?
a. ( s=(n + 2)\times90^{circ} )
b. ( s=(n - 2)\times180^{circ} )
c. ( s=n\times180^{circ} )
d. ( s=n\times90^{circ} )

Explanation:

Step1: Recall polygon interior angles formula

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

Step2: Analyze each option

• Option a: \(S=(n + 2)\times90^{\circ}\) is incorrect.
• Option b: \(S=(n - 2)\times180^{\circ}\) is correct.
• Option c: \(S=n\times180^{\circ}\) is the sum of interior angles of \(n\) - triangles with a common vertex (but not the formula for polygon interior angles sum).
• Option d: \(S=n\times90^{\circ}\) is incorrect.

Answer:

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