![]() ![]() Our polygon with 150 degree interior angles (and 30 degrees exterior angles) has 12 sides.īy the way, a geometric figure with 12 sides is called a dodecagon. That's because they form supplementary pairs (interior+exterior=180).īefore example 4, we learned that we can also calculator the measure of an exterior angle in a regular polygon as 360/x, where x is the number of sides. but the whole problem is that we don't know the number of sides yet OR the sum!īut, because the measure of each interior angle is 150, we also know the measure of an exterior angle drawn at any vertex in terms of this polygon is 180 - 150 = 30. We'd have to multiply by the number of angles to find the sum. But, this time we only know the measure of each interior angle. Previously we identified the number of sides in a polygon by taking the sum of the angles and using the S=(x-2)*180 formula to solve. If the measure of each interior angle of a regular polygon is 150, find the number of sides of the polygon. We now know that interior and exterior angles are supplementary (add up to 180) at each vertex, so the measure of each exterior angle is 180 - 120 = 60. There are six angles in a hexagon, and in a regular hexagon they are all equal.
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