Question

The opposite angels of a parallelogram are ( 30 + x) and ( 15 x + 7 ).Find all the angles of parallelogram?

Answer 1

Opposite angles of a parallelogram are equal
15x+7 =30+x
15x-x =30-7
14x = 23
x=23/14
x= 1.642

angle A =15x+7 = 15 ×1.642+7= 24.63+7 = 31.63
angle C =30+x =30 +1.642 =31.642

AD is parallel to BCand AB is a transversal
angle A +angle B=180 ( co- interior angle)
31.63 +angle B=180
angleB= 180 -31.63
angle B=148.37

AD PARALLEL TO BC AND DC IS A TRANSVERSAL
angle D+angleC =180 (co-interior angle)
angle D+31.642 =180
angle D = 180 -31.642
angle D =148.358

Answer 2

In a parallelogram the opposite angles are equal
So, (30 + x) = (15 x + 7)
       30 + x = 15 x + 7
  ( sending x to RHS and 7 to LHS we get )
        30 - 7 = 15 x - x    
          23 = 14 x
           23 / 14 = x
            1.64  or 1.6 (approx)
         So the angles are ( 30 + x ) = 31.6 (approx)
                                       (15 x + 7 ) = 15 x 1.64 + 7 = 31.6
                                                                                                                                 Sum of all the angles in a quadrilateral is 360
     The remaning two angles are also equal
 So, 2 x + 31.6 + 31.6 = 360
       2 x + 63.2 = 360
       2 x = 360 - 63.2
       2 x = 296.8
         x = 296.8 / 2
         x = 148.4 

So all the angles are 148.4 , 148.4 , 31.6 , 31.6