Question

For the diagram above, if $CD$ is parallal to $GE$ and $AB$ is parallel to $GH$, then $(x+y{)}^{\circ }=$

• A. ${70}^{\circ }$
• B. ${80}^{\circ }$
• C. ${75}^{\circ }$

Answer 1

The correct option is A ${70}^{\circ }$

Given $CD$ aprallel to $GE$ and $AB$ parallel to $GH$.
Now, $\angle ADC$ and $\angle DFE$ are corresponding angles.
$\Rightarrow \angle ADC=\angle DFE$ ($\because CD$ is parallel to $GE$).
$\therefore \angle DFE={120}^{\circ }$
Now, $\angle DFE$ and $\angle EFB$ are lying on the same line.
$\Rightarrow \angle EFB+\angle DFE={180}^{\circ }$
$\Rightarrow x^{\circ }={180}^{\circ }-{120}^{\circ }={60}^{\circ }$
$\because AB$ is parallel to $GH$
$\Rightarrow \angle EFB=\angle FGH={60}^{\circ }$
$\Rightarrow 3y^{\circ }+{30}^{\circ }={60}^{\circ }$
$\Rightarrow 3y^{\circ }={30}^{\circ }\Rightarrow y^{\circ }={10}^{\circ }$
$\therefore (x+y{)}^{\circ }={60}^{\circ }+{10}^{\circ }={70}^{\circ }$