Question 557284
Hi,


Here are a few reminders about solving the problem:

1) angle sum of parallelogram=360 degrees

2) opposite angles of parallelogram are equal in size

3) sum of interior angles of parallelogram=180 degree


Very unfortunately, the question didn't tell you whether angle A and angle B are a pair of opposite angles or interior angles. So you need to try it out yourself.


Firstly, assume angle A and angle B are a pair of opposite angles. Therefore,


        x+6=2x+15
       2x-x=6-15
            x=-9.


However, let's calculate the size of angle A in this case.


Sub x=-9,
 angle A=x+6
              =-9+6

              =-3 ,which is impossible to be an angle.

Now ,the conclusion is: angle A and angle B are a pair of interior angles. Therefore,

   (x+6)+(2x+15)=180
                       3x=180-21
                         x=53


so,angle A=x+6
                   =59.






If angle A and angle D are a pair of opposite angles,
   Therefore angle A=Angle D 
                     Angle D=x+6
                                  =53+6
                                  =59
                                     


If angle A and angle D are a pair of interior angles,
                     
 Therefore angle A+Angle D =180
                              59+angle D = 180
                                     Angle D=121


Angle D can be 59 or 121 degrees.

Ans. D


Cheers,
Heil