# The angles in an #n#-sided polygon satisfy an arithmetic sequence with #a_1 =143^@# and #d=2#. Given that all of the internal angles of the polygon are less than #180^@#, how do I find #n#?

##### 1 Answer

Using

There are 18 sides,

#### Explanation:

Think about the size of the angles.

If

The last term

So there may be

We can check this by finding the sum of the first

Adding an odd number of odd angles (

The sum is not

Let's check with

Sum interior angles =

Thus