Question

in the given figure ABCD is a cyclic quadrilateral and angle ABP is 30° and x is equal to 2 Y find the value of x and y and angle ADC

Answer 1

Answer:In ABCD is cyclic quadrilateral. So ∠ABC + z = 180°

At B, ∠ABC = 180 - 60° = 120°

=> z = 60°

As Arc ABC makes ∠AOC at O and ∠ z at D on the circle,

∠AOC = 2 z = 120°

In ΔBCQ, ∠BCQ = 180° - y - 60° = 120° - y

Hence, at C, ∠BCD = 180° - ∠BCQ = 60° + y

In ΔAPB, ∠PBA = 180° - ∠ABC = 60°

∠PAB = 180° - x - 60° = 120° - 2 y

Hence, ∠DAB = 180 - ∠PAB = 60° + 2y

In the cyclic quadrilateral ABCD, ∠DAB + ∠BCD = 120° + 3 y = 180°

So, y = 20° & x = 40°