Question

Solve for x.



Enter your answer in the box.

x = __°

Answer 1

This is a pentagon, a 5-sided polygon.
There is a formula to find the sum of the measures of the interior angles of a polygon of n sides. It is:

(n - 2)180

A pentagon has 5 sides, so the sum of the measures of the interior angles is

(5 - 2)180 = 3 * 180 = 540

The sum of the measures is 540.

We have every angle measure except the one marked x, but we know the sum all all 5 angle measures is 540.

100 + 102 + 108 + 121 + x = 540

431 + x = 540

Subtract 431 from both sides.

x = 109°

Answer 2

Since we know that there are always 540 degrees in the total interior angles of any polygon, we know that the answer must be:
x = 540 - (121+100+108+102)
x = 540 - 431
x = 109.
Hope this helps!