ABCD is a cyclic trapezium with AD||BC. If ∠ B =70°, determine other three angles of the trapezium.

Question

ABCD is a cyclic trapezium with AD||BC. If &#x2220; B =70&#xB0;, determine other three angles of the trapezium.

Philoid · Accepted Answer

Given that,

ABCD is a cyclic trapezium with AD ‖ BC and ∠B = 70^o

Since, ABCD is a quadrilateral

Then,

∠B + ∠D = 180^o

70^o + ∠D = 180^o

∠D = 110^o

Since, AD ‖ BC

Then,

∠A + ∠B = 180^o (Co. interior angle)

∠A + 70^o = 180^o

∠A = 110^o

Since, ABCD is a cyclic quadrilateral

Then, ∠A + ∠C = 180^o

110^o + ∠C = 180^o

∠C = 70^o