Question

In the given figure, $ABCD$ is a trapezium. $FG$ and $EC$ are straight lines. Find $\angle GBC$.

• A. ${70}^{\circ }$
• B. ${105}^{\circ }$
• C. ${150}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${105}^{\circ }$

$AB$ is parallel to $CD$.

$\therefore \angle ABC+\angle BCD={180}^o$ (Co-interior angles)

$\Rightarrow {30}^o+\angle GBC+{45}^o={180}^o$

$\Rightarrow \angle GBC={180}^o-{75}^o={105}^o$