0

# How do you find the sum of the measures of the angles of a quadrilateral?

Updated: 11/5/2022

Wiki User

14y ago

I'm not sure if you mean interior or exterior angles, so I'll give you an answer for both.

For interior angles:

The sum of the measures of the *interior* angles of a quadrilateral is always 360 degrees. To understand why this is true, recall that the sum of the interior angles of a triangle is 180 degrees. Now, in any quadrilateral, we can draw a diagonal, splitting it into two triangles.

So, the sum of the interior angles of the quadrilateral will be the sum of all of the interior angles of the two triangles, in other words, 2x180.

In general, an n-gon can be divided into n-2 triangles, so the sum of the interior angles of an n-gon is 180x(n - 2) = 180xn - 360

For exterior angles:

The sum of the exterior angles of any closed, convex figure will be 360 degrees. So, if the quadrilateral is convex (isn't bent inwards) the sum of the exterior angles will be 360 as well.

Wiki User

14y ago