How do you get the sum of interior angles of a shape?

Answer 1

This was taught to me in 1952:

"The sum of the interior angles of an n-sided polygon is (2n - 4) right angles"

So double the number of sides, subtract 4 and multiply your answer by 90o

Maybe an easier one to remember: (n - 2) x 180°.

Here's why it might be easier: Note that a triangle has 180°. A polygon must have at least 3 sides (triangle): hence n - 2 is the smallest one you can have. If n = 2 then (n-2 = 0) so you have 0° (not a polygon). With n=3, (n-2 = 1), so you have 180°.

• n = 4: 180° x (4-2) = 360°
• n = 5: 180° x (5-2) = 540°

And so on.