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

Answer:

45 degrees

Step-by-step 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