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Question
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
Options
20°
50°
60°
70°
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Solution
In the given figure, EC || AB,∠ECD = 70° and ∠BDO= 20°. We need to find ∠OBD.
Here, EC || AB and CD is the transversal, so using the property, “corresponding angles are equal”, we get
∠AOD = ∠ECD
∠AOD = 70°
Also, using the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, in ΔOBD, we get,
∠AOD = ∠OBD + ∠BDO
70° = ∠OBD + 20°
∠OBD = 70° - 20°
∠OBD = 50°
Thus,∠OBD = 50° .
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