In the circle, reflex ∠AOC=xo,∠ABC=yo. OABC is a parallelogram, then which of the following is the value of y?

Consider the given figure,

From the figure,
x- Central angle.
y- Inscribed angle.
We know that,
Central angle is twice the inscribed angle.
Then,

x = 2 y

∠ AOC = 360 ° - x

∠ AOC = 360 ° - 2 y

Here,

ABCD

is a parallelogram. And in a parallelogram sum of adjacent angles is

180^{o}

.
Then,

∠ BCO + ∠ AOC = 180^{o}

\Rightarrow ∠ BCO + 360 ° - 2 y = 180^{o}

\Rightarrow 2 y = ∠ BCO + 360 ° - 180^{o}

\Rightarrow 2 y = ∠ BCO + 180^{o}

\Rightarrow ∠ BCO = {2 y - 180}^{o}

Similarly,

∠ ABC + ∠ BCO = 180^{o}

\Rightarrow y + 2 y - 180 ° = 180 °

\Rightarrow 3 y = 360^{o}

\Rightarrow y = 120^{o}

Hence, the value of

y

120^{o}

.
Therefore, option 2 is correct.

In the circle, reflex $∠ AOC = x^{o}, ∠ ABC = y^{o}$ . $OABC$ is a parallelogram, then which of the following is the value of $y$ ?