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Question

In the given figure, ABCD is a cyclic quadrilateral in which AB||DC and BAD=100. Then, ABC=?

(a) 80

(b) 100

(c) 50

(d) 40


Solution

ANSWER:
( b ) 100°
Since ABCD is a cyclic quadrilateral, we have:
BAD + BCD = 180° (Opposite angles of a cyclic quadrilateral)
⇒ 100 ° + BCD = 180°
BCD = (180° - 100°) = 80°
Now, AB || DC and CB is the transversal.
ABC + BCD = 180°
ABC + 80° = 180°
ABC = (180° - 80°) = 100°

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