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

2 Answers
Jan 29, 2016

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#

Jun 3, 2017

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.)