The diagonal of the rectangle forms 40 degrees on one of the sides. Find the angles formed

The diagonal of the rectangle forms 40 degrees on one of the sides. Find the angles formed by the intersection of the diagonals.

Since the diagonals in the rectangle are equal and at the point of intersection, they are divided in half, then ОА = ОD = OC = ОВ, which means that the triangles AOD, DOC, BOC, AOB are equilateral. The angle ADO = DAO = 40. Then the angle AOD = 180 – 40 – 40 = 100. The angle AOD and AOB are adjacent angles, the sum of which is 180, then the angle AOB = 180 – 100 = 80.

Angle BOC = AOB = 100, angle COD = AOB = 80 as vertical angles.

Answer: The angles formed at the intersection of the diagonals are 100 and 80.




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