guerrero wrote:The measures of the interior angles in a polygon are consecutive integers. The largest angle measures 110 degrees. How many sides does this polygon have?
Plugging answer choices is a good strategy for this problem.
As that has been discussed, I'll post another two methods to solve this problem.
Tricky Approach:
If a polygon has n sides, the sum of the interior angles of the polygon = (n - 2)*180°
Hence, the sum must be a multiple of 10, i.e. units digit of the sum must be 0.
As the largest angle measures 110° and the angles are consecutive integers, the next angles will be 109°, 108°, ... etc
The 1st time we get zero as units digit when we start adding the units place of these measures is (0 + 9 + 8 + 7 + 6) ---> Hence, 5 angles --> n = 5
The 2nd time we get zero as units digit when we start adding the units place of these measures is (0 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 + ...) ---> Hence, more than 11 angles angles --> n > 11
Hence, the polygon has 5 sides.
The correct answer is A.
