enigma123 wrote:

The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

A) 8

B) 9

C) 10

D) 11

E) 13

Please help.

Note that the formula for the sum of the angles of a polygon is (n-2)*180

Therefore, the sum of the angles must end in zero

Now, let's start adding until we get units digit zero and then check if it satisfies

136+137+138+139 = We get digit zero

But if we ply (4-2)(180) = 360 this obviously doesn't satisfy cause 136+137...+139 is more than 360. So let's keep trying

+141+142+143+144...another digit 0

Let's see we now have 9 numbers so 180*7 = 1260

We then grab the median of the consecutive integers which is 140*9 = 1260

It satisfies so answer is thus B

Hope it helps

Cheers!

J