Diagonals of rectangle ABCD intersect at point O. Find the angle between the diagonals

| April 13, 2021 | education

The diagonals of the rectangle ABCD intersect at point O. Find the angle between the diagonals of the parallelogram angle DCO = 40 °

At the beginning of the problem, we are talking about a rectangle, so we will solve from the point of view that ABCD is a rectangle.

Let’s denote one of the angles between the diagonals of the rectangle as <COD, and consider the triangle COD. It is known by the condition <DCO = 40 °.
But given that the diagonals in the rectangle are equal, their halves are also equal, DO = CO, which means that the DCO triangle is isosceles.
This means that the angles of such a triangle at the base DC are equal. <CDO = <DCO = 40 °. Now you can find the angle between the diagonals: <COD = 180 – (<CDO + <DCO) = 180 – (40 ° + 40 °) = 100 °



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