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1.) Find the sum of interior angles of a polygon, which has 16 sides |
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| Hint: ViewNumber of sides n = 16, Sum of interior angles of a polygon = (n - 2) x 180, Sum = (16 - 2) x 180 = 14 x 180 = 2520 |
2.) Find the number of sides of a polygon, if the sum of its interior angle is 1620 |
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| Hint: ViewSum of interior angles of a polygon = (n - 2) x 180 = 1620, n - 2 = 1620/180, n = 9 + 2 = 11 |
3.) Is it possible to have a polygon, whose sum of interior angles is 1030. |
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| Hint: ViewSum of interior angles of a polygon = (n - 2) x 180 = 1030, n - 2 = 1030/180, n = 5.72 + 2 = 7.72 which is not a whole number. Therefore, it is not a Polygon. |
4.) One angle of a quadrilateral is 90 and all other angles are equal; find each equal angle |
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| Hint: ViewSuppose all the three angle of a quadrilateral be x, The sum of angles of a quadrilateral = 360, x + x + x + 90 = 360, 3x + 90 = 360, 3x = 270, x = 270/3 =90, The measure of each angle = 90. |
5.) If angles of quadrilateral are in the ratio 4: 5: 3: 6; find each angle of the quadrilateral. |
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| Hint: ViewSuppose the angles of quadrilateral be 4x, 5x, 3x, 6x. The sum of angles of a quadrilateral = 360. 4x + 5x + 3x + 6x = 360, 18x = 360, x = 360/18 = 20. 4x = 4 x 20 = 80, 5x = 5 x 20 = 100, 3x = 3 x 20 =60, 6x = 6 x 20 = 120. Therefore, the angles of the quiadrilateral are 80, 100, 60 and 120. |
6.) Two angles of a hexagon are 90 and 110. If the remaining four angles are equal, find each angle. |
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| Hint: ViewThe sum of interior angle of polygon is (n - 2) x 180.Sum = (6 - 2) x 180 = 4 x 180 = 720. The sum of interior angles of hexagon is 720. hence, 90 + 110 + x + x + x + x = 720, 200 + 4x = 720, 4x = 720 - 200, 4x = 520, x = 520/4 = 130. Hence, the measure of each equal angle = 130. |
7.) Find the number of sides in a regular polygon, if its each interior angle is 160 |
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| Hint: ViewLet the number of sides of a regular polygon = n. Each interior angle = 60, The sum of interior angle of polygon can be calculated as, (n - 2)x 180 /n = 160, (n - 2) x 180 = 160 x n, 180n - 360 = 160n, 180n - 160n = 360, 30n = 360, n = 360/30, We get, n = 12, Hence, the number of sides = 12. |
8.) Find number of sides in a regular polygon, if its each exterior angle is 30. |
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| Hint: Viewlet us assume the number of sides be n. Each exterior angle = 30, Each exterior angle of polygon = 360/n. Now , we have 360/n = 30. n = 360/30 = 12. Hence, the number of sides = 12. |
9.) Which polygon has both its interior and exterior angles the same |
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| Hint: ViewWe know that , Interior angle + Exterior angle = 180 degrees, If Interior angle = Exterior angle, Then, Exterior angle + Exterior angle = 180 degrees, 2 Exterior angle = 180 degrees, Exterior angle = 180/2, Exterior angle = 90. But, Interior angle = Exterior angle = 90, Number of sides n = 360/ (180-Interior angle), n = 360/(180 - 90), n = 360/90, n = 4 A polygon with 4 sides has both interior angles and exterior angles as same. |
10.) Find the measure of each angle of a regular Nonagon |
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| Hint: ViewNumber of sides given is 9, Formula for each interior angle is (n - 2) x 180/n = (9 - 2) x 180/9 = 7 x 180/9 = 140. |
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