Question

In a given figure, ABCD is a cyclic quadrilateral. If angle BAD equal to 52 degree, angle BCAequal to 35 degree. Find angle ACX. Prove that angle CBDequal to angle ADB. Also prove that DX equal to BX. Prove that triangle XBD is an isosceles triangle. Prove that XA equal to XC.

Answer 1

it is known to us that in a cyclic quadrilateral opposite angles are supplementary 
∴∠bad+∠bcd=180 degree
⇒∠bad+∠bca+∠dca=180 degree
now putting the vaues
⇒52 degree+35 degree+∠dca=180
∴∠dca=180°-(52°+35°)
∴∠dca=93