The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8 . Find the smallest angle of the quadrilateral? Given ratio of angles of quadrilateral A B C D is 2 : 3 : 5 : 8 Let the angles of quadrilateral A B C D be 2 x , 3 x , 5 x , 8 x , respectively. We know, by angle sum property, the sum of angles of a quadrilateral is 3 6 0 o . ⇒ 2 x + 3 x + 5 x + 8 x = 3 6 0 o ⇒ 1 8 x = 3 6 0 o ∴ x = 2 0 o . ∴ ∠ A = 2 x = 2 × 2 0 o = 4 0 o , ∠ B = 3 x = 3 × 2 0 o = 6 0 o , ∠ C = 5 x = 5 × 2 0 o = 1 0 0 o and ∠ D = 8 x = 8 × 2 0 o = 1 6 0 o . ∴ The smallest angle = 4 0