Which formula gives the measure of interior angles of a polygon with n sides?

Which formula gives the measure of interior angles of a polygon with n sides?

• A. S=n*180
• B. A=bh/2
• C. S=(n-2)180
• D. P=n+s

Answer: (C)

The total measure of interior angles in an n-sided polygon comes from how many triangles fit inside. An n-sided polygon can be split into n−2 triangles, and each triangle has interior angles adding up to 180 degrees. So the whole polygon contributes (n−2) × 180 degrees to the sum of its interior angles. That’s why the formula for the total interior angle measure is S = (n−2) × 180 degrees. For example, a pentagon (n = 5) has (5−2) × 180 = 540 degrees in total. If you ever want the measure of each interior angle in a regular polygon, you’d divide by n, giving ((n−2) × 180) / n. The other expressions don’t match this relationship, since they either describe area, or don’t connect to the angle-sum idea.

The total measure of interior angles in an n-sided polygon comes from how many triangles fit inside. An n-sided polygon can be split into n−2 triangles, and each triangle has interior angles adding up to 180 degrees. So the whole polygon contributes (n−2) × 180 degrees to the sum of its interior angles. That’s why the formula for the total interior angle measure is S = (n−2) × 180 degrees. For example, a pentagon (n = 5) has (5−2) × 180 = 540 degrees in total. If you ever want the measure of each interior angle in a regular polygon, you’d divide by n, giving ((n−2) × 180) / n. The other expressions don’t match this relationship, since they either describe area, or don’t connect to the angle-sum idea.