diagonals AC and BD intersect at point O,
the angle ABO is 44 °.
Find: Angle AOD
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 °.
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