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

Question

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

Philoid · Accepted Answer

Given: ABCD is a cyclic quadrilateral, AB||DC and ∠BAD = 100°

Here,

∠BAD + ∠BCD = 180° (opposite angles in cyclic quadrilateral are supplementary)

100° + ∠BCD = 180°

∠BCD = 180° – 100°

∠BCD = 80°

Here, AB||DC and BC is the transversal

∠ABC + ∠BCD = 180° (interior angles along the transversal are supplementary)

∠ABC + 80° = 180°

∠ABC = 180° – 80° = 100°

∴ ∠ABC = 100°