If ABCD is a cyclic quadrilateral in which AD || BC (fig. 16.180). Prove that ∠ B= ∠ C .

Question

If ABCD is a cyclic quadrilateral in which AD || BC (fig. 16.180). Prove that &#x2220; B= &#x2220; C .

Philoid · Accepted Answer

Since, ABCD is a cyclic quadrilateral with AD ‖ BC

Then,

∠A + ∠C = 180^o (i) (Opposite angles of cyclic quadrilateral)

And,

∠A + ∠B = 180^o (ii) (Co. interior angles)

Comparing (i) and (ii), we get

∠B = ∠C

Hence, proved