Question

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. ${90}^{\circ }$

Answer 1

The correct option is B ${75}^{\circ }$


ABCD is a parallelogram
Therefore, $\angle ADC=\angle ABC={105}^{\circ }$[Opposite angles of a parallelogram are equal]
$\angle ABC+\angle CBE={180}^{\circ }$ [Linear pair]
$\angle CBE={180}^{\circ }-{105}^{\circ }={75}^{\circ }$
Hence, $\angle CBE={75}^{\circ }.$