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Question 68
In quadrilateral $$ABCD, \angle C = 72^\circ$$ and $$\angle D = 28^\circ$$. The bisectors of $$\angle A$$ and $$\angle B$$ meet in O. What is the measure of $$\angle AOB$$?
Solution
In quadrilateral $$ABCD$$,
$$\angle A +Â \angle B +Â \angle C +Â \angle D$$ = 360
$$\angle A + \angle B = 360 - 72 - 28 = 260\degree$$
$$\frac{1}{2}(\angle A + \angle B) =Â 130\degree$$
In $$\triangle$$ AOB,
$$\frac{1}{2}(\angle A + \angle B) + \angle AOBÂ = 180$$
$$\angle AOB = 180 - 130 = 50\degree$$
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