If one of the angles formed by diagonals and adjacent sides of a rhombus is 20`. Find the four angles of the rhombus. Share with your friends Share 3 Manbar Singh answered this Let ABCD is a rhombus, in which AC and BD are the diagonals that intersect each other at point O.We know that diagonals of rhombus bisect each other at right angle.So,OA = OC and OB = OD∠AOB = ∠BOC = ∠COD = ∠DOA = 90°Let ∠OAB = 20°In ∆AOB and ∆AOD, ∠AOB = ∠AOD 90° each AB = AD sides of rhombus are equal AO = AO common ∆AOB ≅ ∆AOD RHS⇒∠OAB = ∠OAD CPCT⇒∠OAB = ∠OAD = 20°⇒∠A = ∠OAB + ∠OAD = 20° + 20° = 40°In ∆OAB, ∠OAB + ∠AOB + ∠OBA = 180° Angle sum property⇒20° + 90° + ∠OBA = 180°⇒∠OBA = 70°Similarly, we get∆AOB ≅ ∆BOC RHS⇒∠OBA = ∠OBC CPCT⇒∠OBA = ∠OBC = 70°Now,∠B =∠OBA + ∠OBC = 70° + 70° = 140°Now, ∠C = ∠A = 40° Opposite angles of rhombus are equal ∠D = ∠B = 140° Opposite angles of rhombus are equal 2 View Full Answer