in a cyclic quadrilateral ABCD; AD=BC, angle BAC=30 degree and angle CBD=70 degree; find angle BCA - Maths -

Question

in a cyclic quadrilateral ABCD; AD=BC, angle BAC=30 degree and
angle CBD=70 degree; find angle BCA

Priyanka Kedia · Accepted Answer

$S i n c e A D = C B, \Rightarrow A B | | D C \Rightarrow ∠ D C B + ∠ A B C = 180^{0} (c o - int e r i o r a n g l e s a r e \sup p l e m e n t a r y) \Rightarrow 80^{0} + ∠ A B C = 180^{0} \Rightarrow ∠ A B C = 100^{0} N o w, i n Δ B C D, ∠ B C A + ∠ C A B + ∠ A B C = 180^{0} \Rightarrow ∠ B C A + 30^{0} + 100^{0} = 180^{0} \Rightarrow ∠ B C A = 50^{0} H e n c e, ∠ B C A = 50^{0}$

in a cyclic quadrilateral ABCD; AD=BC, angle BAC=30 degree and angle CBD=70 degree; find angle BCA.