find the # of sides of a regular polygon: interior angles measure of 140 degrees?

Answer 1

It must be a nonagon (9 sides), Here's why:

Obviously, the interior angle of 140° must refer to the angle created by the adjacent sides of the polygon. It cannot refer to the number of degrees in each of the congruent triangles forming the polygon, because any triangle has a total measure of 180°. Nor can it refer to the measure of each central angle contained in all of the triangles making up the polygon, because 140 does not divide 360 evenly.

A line drawn from the center of any regular polygon to any of its vertices bisects each of the angles formed by adjacent sides. So each triangular piece of this polygon has two equal base angles of 140°/2 = 70°. Then the central angle of each of these triangles is 180° - 2(70°) = 180° - 140° = 40°. Since a complete cycle around all of the central angles is 360°, then there are 360°/40° = 9 equal or congruent triangles which make up the polygon.

So this regular polygon has 9 sides.

Answer 2

360 degrees in a circle, 140 plus 140 plus 140. that means it only has 3 corners and must be a.............

Answer 3

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