Question

in figure, AB and CD are two diameters of the circle with center O, DE and AB when produced meet at F.. if angle AOD=85 and angle DCE=35, find- 1) angle CDE 2)angle AFD

Answer 1

Given : AB and CD are diameters

so AB = CD

Proof : CD is the diameter and diameter subtends

90 degree at circle , so <DEC = 90 degree

now in triangle CED,

35 + 90+ CDE = 180

CDE= 180 - 125

CDE = 55

now in triangle FOD,

FOD + ODF + DFO = 180. ( ODF = CDF)

180 - 85 + 55 + DFO = 180

95 + 55 + DFO = 180

DFO = 180 - 150

DFO = 30

so, angle CDE = 55

angle DFO = 30

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