Question

In a polygon with 100 sides, 99 of the angles add up to 17,595°. What is the measure of the last angle?

Answer 1

45 degrees

Explanation:

The formula to find the sum of all the interior angles in an "n-gon" (n is a variable that stands for the numbers of sides, ex) 20-gon --> 20 sided polygon) is
`180(n-2)`.

Let's plug in 100 to find the sum of all the interior angles in a 100-gon.

`180(100-2)`

I would rather distribute than simplify the parentheses and have to multiply 180 by 98.

So:

`18000-360`

=
`17640` degrees

[REMEMBER, IT WAS NOT GIVEN THAT THIS POLYGON IS REGULAR, SO DO NOT DIVIDE 17640 BY 100]

Now to find the last angle, we can just subtract since we are given the value of 99 of the 100 angles (17595 degrees).

So the last angle is
`17640-17595=45` degrees