If its a regular 9 sided polygon then the exterior angles are 40 degrees.
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Since the interior angle measure of the regular polygon is 140⁰, its exterior angle measure is 180⁰ - 140⁰ = 40⁰. Since the sum of the exterior angle measures is 360⁰, the polygon has 360⁰/40⁰ = 9 sides.
Interior angle = 140 deg so exterior angle = 40 deg. Sum of exterior angles = 360 so 360/40 = 9 such angles required. So the figure has 9 sides.
To find the interior angle of a polygon, you can use the formula: (n-2) * 180 / n, where n is the number of sides. For a 9-sided polygon, the formula would be (9-2) * 180 / 9, which simplifies to 7 * 180 / 9 = 1260 / 9 = 140 degrees. Therefore, the interior angle of a 9-sided polygon is 140 degrees.
If each interior angle is 171 degrees then each exterior angle is 180-171 = 9 degrees. Sum of all exterior angles (irrespective of number of sides) is 360 degrees So number of sides = 360/9 = 40