The formula for the sum of the interior angles
of a polygon with n sides is
(n - 2)180°
We set that equal to 1800°
(n - 2)180° = 1800°
Divide both sides by 180°
n - 2 = 10
n = 12
So the polygon has 12 sides, and therefore
12 interior angles.
Since one of the angles is 172°,
the other 11 interior angles must have sum
1800°-172°=1628°
Since they are all congruent, we divide 1628°/11 = 148°.
So each of the other 11 interior angles measures 148°.
So it's a 12-sided polygon. I'll draw it with the 172°
angle at the top. 172° is close to 180°, so it looks almost
like the the two sides at the top form a straight line,
but they don't. I'll color the sides of the 172° angle red
and green, so it will look like a 12-sided polygon, not
a 11-sided one. Here's what it looks like:
Edwin
