ABCD rectangle. angle ABD = 60.O-intersection point of AC and BD find the angle DOC.

Let’s write the data.
Given: ABCD – rectangle; angle ABD = 60 °; т. О – the point of intersection of the diagonals; AC and BD are the diagonals of the rectangle.
Find: corner DOC.
Solution:
Since ABCD is a rectangle, angle A = angle B = angle C = angle D = 90 °.
By the property of the rectangle ВС || AD and AB || CD.
Angle ABD = angle BDC = 60 ° – as crossed with parallel straight lines BC and AD and secant BD.
Angle OCD = angle ODC = 60 ° – as angles at the base in an isosceles triangle.
So DOC angle = 180 ° – (OCD angle + ODC angle) = 180 ° – (60 ° + 60 °) = 180 ° – 120 ° = 60 °.
DOC angle = 60 °.
Answer: 60 °.