What are the angle measurements of a icosagon?

Answer 1

First of all, I'm going to assume you mean the interior angles.

Secondly, I'm going to assume you mean a regular icosagon (regular means that all the angles and sides are equal in measure).

As an example, a square is a regular quadrillateral. Each angle is the same, which for a square is 90 degrees.

An icosagon is a 20-sided figure. I assume the asker knows this, but for someone reading who isn't familiar with it, that is important.

The total degree measure of any polygon's interior angles always adds up to a constant value. The thought process is simple: for a triangle, the angles add up to 180 degrees. For a quadrillateral, it's just 2 triangles, so 2*180=360 degrees. For each side you add, that's one more triangle it could be divided into. So, as a general formula, it's 180(n-2) where n is the number of sides. That's the total angular measure. So, to get each individual angle, you have to divide by the number of sides, which gets you 180(n-2)/n.

Back to the question. In this case, n=20. So each angle would be 180(20-2)/20=162.

Each angle in a regular icosagon will measure 162 degrees.

Side note: if the icosagon isn't regular, the angles will still average out to 162 degrees.