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Question
In the given figure, if AB || CD, then x =
Options
100°
105°
110°
115°
Solution
100°
Explanation:
The given figure is as follows:
It is given that AB || CD.
Let us draw a line PQ parallel to AB and CD.
It is given that,
∠1 + ∠2 = 148° ...(i)
Since, AB || PQ Thus, ∠APQ angle and ∠1 are consecutive interior angles.
Therefore,
∠1 + 132° = 180°
∠1 = 180° − 132°
∠1 = 48° ...(ii)
Similarly, CD || PQ. Thus, x angle and ∠2 are corresponding angles.
Therefore,
∠2 = x ...(iii)
On substituting (ii) and (iii) in (i):
48° + x = 148°
x = 148° − 48°
x = 100°
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