Given table is: Each exterior angle of a regular polygon with n sides is 360 ° n . Each interior angle of a regular polygon with n sides is n - 2 × 180 ° n . (i) Given n = 6 . Each exterior angle is = 360 ° 6 = 60 ° . Each interior angle is = 6 - 2 × 180 ° 6 = 4 × 30 ° = 120 ° . (ii) Given n = 8 . Each exterior angle is = 360 ° 8 = 45 ° . Each interior angle is = 8 - 2 × 180 ° 8 = 6 × 180 ° 8 = 1080 ° 8 = 135 ° (iii) Given each exterior angle is 36 ° . Each exterior angle = 360 ° n . ⇒ 36 ° = 360 ° n ⇒ n = 360 ° 36 ° = 10 The number of sides is 10 . Each interior angle is = 10 - 2 × 180 ° 10 = 8 × 18 ° = 144 ° . (iv) Given each exterior angle is 20 ° . Each exterior angle = 360 ° n . ⇒ 20 ° = 360 ° n ⇒ n = 360 ° 20 ° = 18 . The number of sides is 18 . Each interior angle is = 18 - 2 × 180 ° 18 = 16 × 10 ° = 160 ° . (v) Given each interior angle is 135 ° . The interior angle is the same as in the case of (ii). Therefore, the number of sides are 8 . Each exterior angle is 45 ° . (vi) Given each interior angle is 165 ° . ⇒ n - 2 × 180 ° n = 165 ° ⇒ n - 2 n = 165 ° 180 ° = 11 12 ⇒ 12 n - 2 = 11 n ⇒ 12 n - 24 = 11 n ⇒ 12 n - 11 n = 24 ⇒ n = 24 . The number of sides is 24 . Each exterior angle is = 360 ° 24 = 15 ° .