In the figure, $ABCD$ is a parallelogram in which $\angle ADC=105^\circ$. The value of $\angle CBE$ is


A) $105^\circ

B) $75^\circ

C) $55^\circ

D) $90^\circ

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The correct answer is Option B, which is $ 75^\circ $.

Given that $ABCD$ is a parallelogram, it follows that opposite angles are equal. Therefore, $$ \angle ADC = \angle ABC = 105^\circ. $$

Since $$ \angle ABC + \angle CBE = 180^\circ $$ (as they form a linear pair), we can compute $\angle CBE$ as follows: $$ \begin{aligned} \angle CBE &= 180^\circ - \angle ABC \ &= 180^\circ - 105^\circ \ &= 75^\circ. \end{aligned} $$

Thus, $\angle CBE = \textbf{75}^\circ$ is the final answer.

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