Question

If measures opposite angles of a parallelogram are (60 − x)° and (3x − 4)°, then find the measures of angles of the parallelogram.

Answer 1

Let ABCD be a parallelogram, with  ∠A = (60 - x )° and∠C = (3x - 4).

We know that in a parallelogram, the opposite angles are equal.

Therefore,

     ∠A = ∠C

60 - x = 3x - 4

 -x 3x = - 4 - 60

   -4x = -64 

 x = 16

Thus, the given angles become

∠A = (60 - x)°

     = (60 - 16)°

     = 44 °

Similarly,

∠C = 44°

Also, adjacent angles in a parallelogram form the consecutive interior angles of parallel lines, which must be supplementary.

Therefore,

∠A +∠B = 180°

44° + ∠B = 180°

          ∠B = 180° - 44°

           ∠B = 136° 

Similarly,

∠D = ∠B

∠D = 136° 

Thus, the angles of a parallelogram are 44°,136°,44° and136° .