In rectangle ABCD, the angle between the diagonal and the side is 30 °. Find: the angles between the diagonals.

Let O denote the point of intersection of the diagonals of this rectangle ABCD.

According to the condition of the problem, the angle between the diagonal and the side of this rectangle is 30 °.

Let this diagonal be the AC diagonal, and the 30 ° angle be the OAB angle.

Consider the triangle AOB.

Since the diagonals of the rectangle are equal and are divided by the point of intersection in half, in this triangle the sides AO and OB are equal.

Therefore, this triangle is isosceles and the OBA angle is also 30 °.

Therefore, the angle AOB is 180 – 30 – 30 = 120 °.

Since the angles AOD and AOB are adjacent, the angle AOD is 180 – ∠ AOB = 180 – 120 = 60 °.

Answer: The angles between the diagonals are 60 ° and 120 °.