The diagonals of rectangle ABCD intersect at point O, the angle ABO is 44 °. Find the corner AOD.

Given:

rectangle ABCD,

diagonals AC and BD intersect at point O,

the angle ABO is 44 °.

Find: Angle AOD

Solution:

Consider the ABO triangle. It is isosceles because the diagonals of the rectangle are equal and the intersection is halved. Then BO = AO and angle ABO = angle BOA = 44 degrees. Hence the angle OAD + angle OAB = angle A;

angle ОАD = 90 – 44;

angle ОАD = 46 °.

Consider triangle ABD. He is isosceles. Then the angle OAD = angle ODA = 46 °. Hence the angle AOD = 180 – (46 + 46) = 180 – 94 = 88 °.

Answer: Angle AOD = 88 °.