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Correct option is D)

Refer figure:

Construct: Join points $B$ and $D$ at $A$ such that $A$ lies on the circumference.

Join $BandD$

Thus, $∠A=21 ×∠O$ ( angle subtended by a chord at the center is twice the angle at the circumference)

thus, $∠A=2140 =70°$

Also, $ABCD$ is a cyclic quadrilateral. Hence, $∠A+Θ=180°$ (sum of opposite angles of a cyclic quadrilateral is 180 degrees)

$Θ=180−70=110°$

In $△OBD$,

$OB=OD$ (radius of circle)

$∠OBD=∠ODB=21 ×(180−140)$ (angles opposite to equal sides are equal)

Hence, $∠OBD=∠ODB=20°$

In $△DCB$

$θ+∠CBD+∠CDB=180°$

$θ+(α−∠OBD)+(β−∠ODB)=180°$

$110°+α−20°+β−20°=180°$

Thus, $α+β=110°$

Summarizing,

$θ=110°$

$α+β=110°$

Thus, both options A&C are correct.

Correct choice : D

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