Question

What do the interior angles of a polygon have to add up to?

Answer 1

See below.

Explanation:

The sum of interior angles of a polygon is equal to

`A =(pi/2)n`

where `n` is the number of triangles needed to compose the polygon.

Occours that the number of triangles is equal to the number of sides minus `2` or

`n = l - 2` where `l` is the number of polygon sides.

The final formula is

`A = (pi/2)(l-2)`

Examples.

A triangle has `l=3` so `A=pi/2`
A quadrilateral has `l=4` so `A=pi`
A heptagon has `l=7` so `A=5(pi/2)`

Answer 2

To determine the sum of the internal angles of a polygon, take the number of sides on the polygon, subtract 2 and multiply by 180 degrees.

Explanation:

A triangle has three sides. `(3-2)*180 = 180`
The sum of the internal angles of a triangle is 180 degrees.

A quad lateral has four sides. `(4-2)*180 = 360`
The sum of the internal angles of a square is 360 degrees.

A pentagon has 5 sides. `(5-2)*180 = 540`
The sum of the internal angles of a pentagon is 540 degrees.

A hexagon has six sides. `(6-2)*180 = 720`
The sum of the internal angles of a hexagon is 720 degrees

A heptagon has seven sides. `(7-2)*180 = 900`
The sum of the internal angles of a heptagon is 900 degrees.

and so on!