The diagonals of the ABCD rectangle intersect at point O. Find the angle between the diagonals if the angle ADO = 54 degrees.

Consider tr. AOD-he is isosceles (BD and AC-diagonals) ==> ODA angle = OAD angle = 54 ==> AOD angle = BOC angle = 180- (54 + 54) = 180-104 = 76 (the sum of the tr. Angles is 180 ) Consider tr.BOA and tr.COD – they are isosceles and equal (BA = CD; angle CDO = angle of OCD; angle ABO = angle BAO y. CDO = y.OCD = 36 (90-54 = 36) (the corners of the rectangle are straight ) y.ABO = y.BAO = 36 y. BOA = y.COD = 180- (36 + 36) = 180-72 = 108
Answer: 76, 108