In a cyclic quadrilateral ABCD if AB||CD and B= 70°, find the remaining angles.

Question

In a cyclic quadrilateral ABCD if AB||CD and B= 70&#xB0;, find the remaining angles.

Philoid · Accepted Answer

Given that,

∠B = 70^o

Since, ABCD is a cyclic quadrilateral

Then,

∠B + ∠D = 180^o

70^o + ∠D = 180^o

∠D = 110^o

Since, AB ‖ DC

Then,

∠B + ∠C = 180^o (Co. interior angle)

70^o + ∠C = 180^o

∠C = 110^o

Now,

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

∠A + 110^o = 180^o

∠A = 70^o