MathematicsIf ABCD is a cyclic quadrilateral with AD parallel to BC. ∠DCB=65o. Then, which of the following is the magnitude of ∠CBE is:

If $ABCD$ is a cyclic quadrilateral with $AD$ parallel to $BC$ . $∠ DCB = 65^{o}$ . Then, which of the following is the magnitude of $∠ CBE$ is:

Consider the given figure,

From the figure-

AD ∥ BC

ABCD

is a cyclic quadrilateral.

∠ DCB = 65^{o}

.
In a cyclic quadrilateral sum of opposite angles are supplementary.
Then,

\Rightarrow ∠ DCB + ∠ DAB = 180^{\circ}

\Rightarrow ∠ DAB = 180^{\circ} - ∠ DCB

\Rightarrow ∠ DAB = 180^{\circ} - 65 °

\Rightarrow ∠ DAB = 115^{\circ}

As,

AD ∥ BC

⟹

∠ DAB = ∠ CBE = 115^{\circ}

...[Corresponding angles].
Hence, the measure of

∠ DAB

115^{\circ}

.
Therefore, option 3 is correct.

JEE