Question

Which of the following can be used to find the sum of the interior angles for

any regular polygon?
A. Multiply the number of sides by 180
B. Add 1 to the number of sides and multiply the sum by 180
C. Subtract 2 from the number of sides and multiply the difference by
180
O D. Divide the number of sides by 180

Answer 1

C

Explanation:

for the sum of interior angles of a polygon, multiply the number of triangles (!) in the polygon by 180°.

as the sum of all angles in a triangle is always 180°.

the number of triangles you get when you pick one vertex and connect it straight with every other vertex.

there you see that you create a triangle with every other vertex except for the 2 neighboring vertexes (where the connection are actual side lines of the polygon).

so, in general, the formula for the sum of interior angles is (n − 2)×180. "n" is the number of sides.