# The diagonal of the rectangle forms an angle of 50 ° from one of its sides. Find the angle between the diagonals of this rectangle

May 31, 2020 | Education

| The diagonals of the rectangle are equal and the intersection point is divided in half (by the property of the rectangle).

Consider the triangle ABO (see figure).

AO = BO (as we just found out).

Therefore, the triangle ABO is isosceles.

By the first property of an isosceles triangle:

∠OBA = ∠OAB

By the theorem on the sum of the angles of a triangle:

180 ° = ∠AOB + ∠OBA + ∠OAB

180 ° = ∠AOB + 50 ° + 50 °

∠AOB = 80 °

Answer: 80

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.