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Maths-

General

Easy

Question

In the given figure, $stack A B with bar on top$ is parallel to CD, then x =

45°
55°
65°
75°

Hint:

In this question, we have to find the value of x using the figure given. For that first we will extended of the parallel line such that they intersect with a common transversal. Later using some common theorems like angle properties of parallel lines or of triangle.

The correct answer is: 65°

Extended CD to G so that it intersect EB at F
Now, GD II AB and EB is transversal
So, $angle$ EFG = $angle$ EBA =140 $degree$ [corresponding angles]
Also, As GD is a straight line.
$angle$ ECG + $angle$ ECD = 180 $degree$ [sum of angles in a straight line is 180 $degree$ ]
$rightwards double arrow$ $angle$ ECG + 105 $degree$ = 180 $degree$
$rightwards double arrow$ $angle$ ECG = 75 $degree$
In $triangle$ ECF,
$angle$ FEC + $angle$ ECF = $angle$ EFG [exterior angle is equal to sum sum of interior opposite angles ]
$rightwards double arrow$ x + 75 $degree$ = 140 $degree$
$rightwards double arrow$ x = 65 $degree$

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