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Question
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
Options
70°
110°
120°
130°
Solution
We have to find the value of ∠ABD in the following figure.
It is given that
∠MAE = 70°
∠NAC = 70°(Vertically apposite angle)
Now ∠MAE + ∠EAB + ∠BAC =180° (linear pair) …… (1)
Similarly ∠EAB +∠BAC +∠NAC = 180° (linear pair) …… (2)
From equation (1) we have
∠EAB + ∠BAC = 180°
= 110°
Now ∠FCA = ∠DBA (same exterior angle)
∠ACF = ∠EAC (Interior angle)
Now
∠EAC = 110°
So ∠AFC = 110°
Since ∠AFC =∠ABD
Hence (b)∠ABD = 110°.
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