The only way to do it is to measure the angles, There is no formula that will give you the measure of an interior angle of any shape unless it happens to be regular. And there is nothing in the question to suggest that the shape might be regular.
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An exterior angle of a regular polygon and its corresponding interior angle = 180° If an exterior angle is 1/8 of the interior angle (A) then A + A/8 = 180 : 9A = 1440 : A = 160 Each exterior angle is thus 180 -160 = 20° The number of sides = 360 ÷ exterior angle = 360 ÷ 20 = 18
A regular polygon has sides of equal length, as well as interior angles of equal measure. But for any regular polygon, the sum of the measures of the exterior angles is 360 degrees. You can use this information to find out the measure of an interior angle, because the sum of the measures of each interior/exterior pair of angles is always 180 degrees. So to find the answer to this problem, divide 360 by 7. Each exterior angle is about 51.4 degrees. Subtract that number from 180. Each interior angle is about 128.6 degrees.
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When a polygon is regular, each exterior angle is equal to the other exterior angles. Since the sum of all the exterior angles is 360 degrees, if you divide 360 by the measure of one exterior angle, you will get the number of sides. If you instead have the measure of an interior angle, simply calculate (180 - interior angle measure) to find the measure of the exterior angle, and use the above paragraph.
360 /each exterior angle