How many angles does a polygon have

How many triangles do you think a 5-sided polygon will have? Here's a pentagon, a 5-sided polygon. From vertex A we can draw two diagonals which separates the pentagon into three triangles. We multiply 3 times degrees to find the sum of all the interior angles of a pentagon, which is degrees. Related Links: Polygon definitions, p olygon formulas area, perimeter and polygon names Tables and Formulas.

All rights reserved. Please read our Privacy Policy. Homework Help Geometry Polygons. Email this page to a friend. First Glance. Problem 1 What is the total number degrees of all interior angles of a triangle? Show Answer. Problem 2 What is the total number of degrees of all interior angles of the polygon?

Problem 3 What is the sum measure of the interior angles of the polygon a pentagon? Problem 4 What is sum of the measures of the interior angles of the polygon a hexagon? A regular polygon is simply a polygon whose sides all have the same length and angles all have the same measure.

You have probably heard of the equilateral triangle , which are the two most well-known and most frequently studied types of regular polygons. Examples of Regular Polygons Regular Hexagon. Regular Pentagon. More on regular polygons here. What about when you just want 1 interior angle? Now, remember this new rule above only applies to regular polygons.

So, the only type of triangle we could be talking about is an equilateral one like the one pictured below.

Problem 5 What is the measure of 1 interior angle of a regular octagon? Problem 6 Calculate the measure of 1 interior angle of a regular dodecagon 12 sided polygon? Problem 7 Calculate the measure of 1 interior angle of a regular hexadecagon 16 sided polygon?

Challenge Problem What is the measure of 1 interior angle of a pentagon? How about the measure of an exterior angle? Problem 8 Calculate the measure of 1 exterior angle of a regular pentagon? Calculate the sum of interior angles in an octagon.

All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is:. Calculate the size of the interior angle of a regular hexagon. If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The formula for calculating the size of an exterior angle is:.

Calculate the size of the exterior and interior angle in a regular pentagon.