Question

In the figure(not drawn to scale), $ABC$ and $DEF$ are two triangles, $CA$ is parallel to $FD$ and $CFBE$ is a straight line. Find the value of $x+y$.

• A. ${185}^o$
• B. ${134}^o$
• C. ${148}^o$
• D. ${176}^o$

Answer 1

The correct option is A ${185}^o$

Given that $CA$ is parallel to $FD$ and $CFBE$ is straight line.

$\angle x=\angle DFE={51}^{\circ }$

In a triangle $\Delta ABC$, we have

$\angle y=\angle x+{83}^{\circ }$ ....Exterior angle property of triangle $ABC$

$\Rightarrow \angle y={51}^{\circ }+{83}^{\circ }$

$\Rightarrow \angle y={134}^{\circ }$

$\angle x+\angle y={51}^{\circ }+{134}^{\circ }={185}^{\circ }$