The measure of $angle F E J$ is ______.

50⁰
60⁰
90⁰
120⁰

hint Hint:

In this question, we have to find the $angle F E J$ , if GI and JH are parallel with transversal GH. as $angle$ IGH and $angle$ CHE are alternate interior angles and so they are equal . Later as in $increment$ CHE, we have the value of two angles, so, we an easily find the value of third angle. Further, as $angle$ CEH and care vertically opposite angles so there values will be equal. So, using this process we can easily get the required value of $angle$ JEF .

The correct answer is: 50⁰

$degree$
As GI and JH are parallel with transversal GH,
$angle$ IGH = $angle$ CHE = 40 $degree$ (alternate interior angles)
In $increment$ CHE,
$angle$ HCE + $angle$ CEH + $angle$ CHE = 180 $degree$
90 $degree$ + $angle$ CEH + 40 $degree$ = 180 $degree$
$angle$ CEH = 180 $degree$ - 130 $degree$
$angle$ CEH = 50 $degree$
As $angle$ CEH and $angle$ JEF are vertically opposite angles
so, $angle$ JEF = 50 $degree$

If l || m then find the measures of x and y?

In this question we have to find x and y given that l is parallel to m and t is the transversal. First to find x we can use linear pair as we know that the sum of angles which are in linear pair is 180 deg. Next to find y we can use the theorem alternate exterior angles are equal.