In the given figure, AB || DE and BD || FG such that =50^ and =12… - Vidyadip

Question

In the given figure, AB || DE and BD || FG such that $\angle\text{ABC}=50^\circ$ and $\angle\text{FGH}=120^\circ.$ Find the value of x and y.

✓

Answer

$\angle\text{FGH}+\angle\text{FGE}=180^\circ$ (linear pair)$\Rightarrow120^\circ+\text{y}=180^\circ$
$\Rightarrow\text{y}=60^\circ$
AB || DF and BD is the transversal.
$\Rightarrow\angle\text{CDE}=50^\circ$
BD || FG and DF is the transversal.
$\Rightarrow\angle\text{EFG}=\angle\text{CDE}$ (alternate angles)
$\Rightarrow\angle\text{EFD}=50^\circ$
In $\triangle\text{EFG},$ by angle sum property,
$\angle\text{FEG}+\angle\text{FGE}+\angle\text{EFG}=180^\circ$
$\Rightarrow\text{x}+\text{y}+50^\circ=180^\circ$
$\Rightarrow\text{x}+60^\circ+50^\circ=180^\circ$
$\Rightarrow\text{x}=70^\circ$

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