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In the given figure, ΔOQP = ΔOAB, angle OPQ = 52° and angle BOQ = 104°. Find angle OAB |
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Answer» Step-by-step explanation:PQ is parallel to ABSo, Angle OPQ = Angle OBA (because, ALTERNATE interior angles)Angle OBA = 52 DegreesAngle QOB = Angle POA = 104 Degrees ( Vertically Opposite Angles) - (1)Angle POQ = Angle AOB ( Vertically Opposite Angles) - (2)Angle(QOB + POA + POQ + AOB) = 360 DegreesAngle(2QOB + 2AOB) = 360 Degrees [ from (1) and (2)]208 + 2 AOB = 3602 AOB = 360 - 208 = 152AOB = 152/2 = 76 DegreesTherefore, Angle AOB + Angle OBA + Angle OAB = 180 Degrees76 + 52 + OAB = 180128 + AOB = 180AOB = 180 - 128 = 52Angle AOB = 52 Degrees |
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