Question

$\text{In the given figure,}AB||DEandBD||FGsuchthat\angle ABC={50}^{\circ }and\angle FGH={120}^{\circ }.\text{Find the values of x and y.}$

Answer 1

ANSWER:
We have, $\angle FGE+\angle FGH={180}^{\circ }$
(Linear pair of angles)
∴ $y+120°={180}^{\circ }$
⇒ $y=180°-120°={60}^{\circ }$
Now, AB || DF and BD is the transversal.
∴ $\angle ABD=\angle BDF$
(Pair of alternate angles)
⇒ $\angle BDF={50}^{\circ }$
Also, BD || FG and DF is the transversal.
∴ $\angle BDF=\angle DFG$
⇒ $\angle DFG={50}^{\circ }$
(Pair of alternate angles)
.....(1)
In $△EFG$,
$\angle FGH=\angle EFG+\angle FEG$ (Exterior angle of a triangle is equal to the sum of the two opposite interior angles)
⇒ ${120}^{\circ }={50}^{\circ }$ + x [Using (1)]
⇒ x = ${120}^{\circ }-{50}^{\circ }={70}^{\circ }$
Thus, the values of x and y are${70}^{\circ }and{60}^{\circ }$, respectively.