If its a regular 9 sided polygon then the exterior angles are 40 degrees.
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.
The formula to find the sum of the angles of a polygon is: 180(n - 2) Since we know that one angle of this regular polygon is 171 degrees, we can find what kind of polygon it will be, using the formula: 180(n - 2) = 171n 180n - 360 = 171n 180n - 171n = 360 9n = 360 n = 360/9 n = 40 Thus the polygon is a 40-sided polygon. Check: 180(40 - 2) = 180(38) = 6840, which is the sum of the angles of the polygon. 6840/40 = 171 degrees, which is the measure of one of the angles of that polygon .
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.
Ah, let's paint a happy little picture of a 9-sided polygon, also known as a nonagon. To find the interior angle of a regular nonagon, we use the formula (n-2) * 180 degrees / n, where n is the number of sides. So for a nonagon, it would be (9-2) * 180 degrees / 9, giving us an interior angle of 140 degrees. Isn't that just delightful?
1, 260 degrees
If its a regular 9 sided polygon then the exterior angles are 40 degrees.
The angle sum of any polygon is 360 degrees.
If each exterior angle is 9 degrees then it is a regular 40 sided polygon.
Each central angle of a regular 9 sided polygon: 360/9 = 40 degrees
1260 degrees
The sum of the interior angles of an n-sided polygon (I presume that's what you mean), in degrees, is 180 * (n - 2). Here, n is 9 so the answer is 7 * 180 which is 1,260 degrees.
140 degrees
If this 9 sided polygon is a regular polygon, then the sum of its angles is:(n - 2)180 degrees = (9 - 2)180 degrees = 7 x 180 degrees = 1,260 degrees.
40
40
360 / 9 = 40