### Instruction: One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?### Response: I need to find the number of sides of the polygon, so I can call it n.
I know that the sum of the interior angles of any convex polygon with n sides is given by the formula (n - 2) * 180 degrees.
Since one angle is 160 degrees and the rest are 112 degrees, I can write an equation for the sum of the angles as: 160 + (n - 1) * 112 = (n - 2) * 180.
I can simplify this equation by expanding the brackets and collecting like terms: 160 + 112n - 112 = 180n - 360.
This gives me: 48 + 112n = 180n - 360.
Subtracting 112n from both sides, I get: 48 = 68n - 360.
Adding 360 to both sides, I get: 408 = 68n.
Dividing both sides by 68, I get: n = 6.
This means the polygon has 6 sides.