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 =

  1. 233    
  2. 292    
  3. 195    
  4. 127    


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, angleFDA = angleFDA + angleFDE = x - 180degree            [angleFDE is 180degree as FDE is a straight line]
    Now, BC II GE and AB is a transversal.
    angleCBA  + angleBFE = 180degree                                       [corresponding angles]
    rightwards double arrowangleBFE + 112degree =180degree
    rightwards double arrowangleBFE = 68degree
    Now, in incrementAFD,
    angleFAD + angleFDA = angleBFD                                   [exterior angle is equal to sum of opposite interior angles]
    rightwards double arrow15degree + x - 180degree = 68degree
    rightwards double arrowx = 233degree