Find the smaller of the angles between the diagonals of the rectangle if its smaller side is 1: 2 to the diagonal.

rectangle ABCE,
AB: AC = 1: 2,
diagonals AC and BE intersect at point O,
Find the degree measure of the angle BOA -?
Solution:
1. Consider a right-angled triangle ABC. Since AB: AC = 1: 2, the BCA angle = 30 degrees. Knowing that the sum of the degree measures of the angles of the triangle is 180 degrees, then the angle BAC = 180 – 90 – 30 = 60 (degrees).
2. Consider the BOA triangle. It is isosceles, since the diagonals in the rectangle are equal and the intersection point is halved. Then the angle ABO = angle ABO = degrees. So the angle BOA = 180 – 60 – 60 = 60 degrees.
Answer: 60 degrees.