Question

In the above figure, DM, HN and EG are parallel lines and AB || CD. Find the value of angle x using the given angles.

Answer 1

Given, $\angle$ MDJ = 120°
$\angle$ BIH= 40°
$\angle MDJ=\angle JGF$= 120°
(Since alternate interior angles are equal)

$\angle JGF+\angle FGC=180°$
(Since both of these angles form a linear pair of angles)

$\Rightarrow \angle FGC=180°-\angle JGF$
$\Rightarrow \angle FGC$ = 180°- 120° = 60°

Now, $\angle BIH$ = $\angle BFE$ = 40°
(Since corresponding angles are equal)

Also, $\angle BFE$ = $\angle GFC$ = 40°
(Since vertically opposite angles are equal)

In $△$ FGC ,
x + 40° + 60° = 180°
(Sum of all the interior angles of a triangle is 180° )
$\Rightarrow$x = 180° - 100° = 80°
$\Rightarrow$ x = 80°