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Question
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
Options
100°
80°
90°
135°
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Solution
In the given problem, line segment AB and CD intersect at O, such that ,AC || DB , ∠CAB = 45° and ∠CDB = 55° .
We need to find ∠BOD
As AC || DB
Applying the property, “alternate interior angles are equal”, we get,
∠OBD = ∠CAB
∠OBD= 55° .......(1)
Now, using the angle sum property of the triangle
In ΔODB, we get,
∠OBD + ∠ODB + ∠BOD = 180°
55° + 45° + ∠DOB = 180° (using 1)
∠BOD = 180 °- 100°
∠BOD = 80°
Thus,∠BOD = 80°
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