Question

In the figure (not drawn to scale), BCF is an isosceles triangle with FC$=$FB, EBF and ABC are straight lines, EB is parallel to GC. Find x.

• A. ${264}^o$
• B. ${84}^o$
• C. ${118}^o$
• D. ${200}^o$

Answer 1

The correct option is A ${264}^o$

$EB$ is parallel to $GC$ .....(given)

$\Rightarrow \angle BCG=\angle ABE={48}^{\circ }$ ....Corresponding angles of parallel lines

$\Rightarrow \angle FBC=\angle ABE={48}^{\circ }$ Vertically opposite angles

In a $\Delta BCF$, we have

$FC=FB$ given

$\Rightarrow \angle FBC=\angle FCB={48}^{\circ }$ ....Angles opposite to equal sides are also equal

Consider point $C$:

Sum of all angles around a point $={360}^{\circ }$.

$\Rightarrow \angle BCG+\angle FCB+\angle x={360}^{\circ }$

$\Rightarrow {48}^{\circ }+{48}^{\circ }+\angle x={360}^{\circ }$

$\Rightarrow {96}^{\circ }+\angle x={360}^{\circ }$

$\Rightarrow \angle x={264}^{\circ }$