The sum of the angle measures of a polygon with s sides is 2,340°. Find s.
The formula for the sum of the angle measures of a polygon is (s-2)(180°), where s is the number of sides.
Setting this equal to 2,340° and solving for s gives (s-2)(180°) = 2,340°.
Expanding the left side gives 180s - 360 = 2,340°.
Adding 360 to both sides gives 180s = 2,700°.
Dividing both sides by 180 gives s = 15.
So, the polygon has 15 sides. Answer: \boxed{15}.