There are formulae for calculating the interior angles of polygons but I can never remember it. I do not have to, as i always start from first principles. This is much easier and safer, in my opinion.
Hopefully everyone knows that the interior angles of any triangle add to 180 degrees.
Quadrilaterals - any 4-sided shape can be cut into 2 triangles... 2 triangles means interior angles add to 2x180 --> 360.
5-sided polygons - all 5-sided polygons can be cut into 3 triangles... 3 triangles means interior angles add upto 3x180 --> 540.
TABLE OF POLYGONS
There is a definite pattern here:
Number of sides_______equivalent
in the Polygon_________no. triangles
This is all you need to remember/know. And yes, for all the mathematicians shouting that this is just the formula anyway. I know it is, but my way means you do not have to remember an abstract formula with n in it...mine comes from knowing something real and then using that fact to get the answer.
EXAMPLE 1 Q Find the sum of the interior angles of a 16-sided polygon.
A A 16-sided shape is equivalent to 14 triangles. So 14x180 = 2520 degrees. DONE with no formula!
EXAMPLE 2 Q Find the value of an interior angle of a 12-sided regular polygon.
A A 12-sided polygon is equivalent to 10 triangles. So 10x180 = 1800 degrees. Now, the polygon is regular which means all the angles are the same... we have 12 angles, so each much be 1800/12 = 150.