Question

What is the sum of the interior angle measures in a 35-gon?

Answer 1

The interior angle of a 35-gon would be `169.71^o`

Explanation:

The equation of the interior angle of an polygon is
`((n-2)180)/n` = interior angle, where n is the number of sides.

A 35-gon has 35 sides.
`((35-2)180)/35`

`((33)180)/35`

`(5,940)/35`

`169.71`

The interior angle of a 35-gon would be `169.71^o`

Answer 2

Sum of the interior angles:

`33 xx 180° = 5940°`

Explanation:

In a convex polygon, if you draw in all of the diagonals from one vertex to all the other vertices, you will form triangles.

The number of triangles will always be 2 less than the number of sides.

If there are `3` sides `rarr 1 Delta`
If there are `4` sides `rarr 2 Delta s`
If there are `5` sides `rarr 3 Delta s`
If there are `9` sides `rarr 7 Delta s`
If there are `20` sides `rarr 18 Delta s`

If there are `35` sides `rarr 33 Delta s`

EACH triangle has `180°` and this will give the sum of the angles in the polygon.

`33 xx 180° = 5940°`

This is exactly why the formula to find the sum of the angles in a polygon is:

`"Sum interior angles" = 180(n-2)`

(`n-2)` is the number of triangles formed from one vertex.

Remember that the sum of the exterior angles is ALWAYS 360°

If you want to find the size of each interior angle, divide the total by the number of sides/angles.

In this case: `5940/35 = 169.7°` (but not asked for.)