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Maths-

General

Easy

Question

In the given figure, $stack B C with bar on top parallel to stack D E with bar on top$ and $A B C equals 112 to the power of ring operator end exponent comma open floor B A D equals 15 to the power of ring operator end exponent close$ then the value of x =

233
292
195
127

Hint:

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

The correct answer is: 233

Extended DE so that it intersect AB at F.
Now, $angle$ FDA = $angle$ FDA + $angle$ FDE = x - 180 $degree$ [ $angle$ FDE is 180 $degree$ as FDE is a straight line]
Now, BC II GE and AB is a transversal.
$angle$ CBA + $angle$ BFE = 180 $degree$ [corresponding angles]
$rightwards double arrow$ $angle$ BFE + 112 $degree$ =180 $degree$
$rightwards double arrow$ $angle$ BFE = 68 $degree$
Now, in $increment$ AFD,
$angle$ FAD + $angle$ FDA = $angle$ BFD [exterior angle is equal to sum of opposite interior angles]
$rightwards double arrow$ 15 $degree$ + x - 180 $degree$ = 68 $degree$
$rightwards double arrow$ x = 233 $degree$

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