Question

The adjacent angles of a parallelogram are (2x – 4)° and (3x – 1)°. Find the measures of all angles of the parallelogram.

Answer 1

Since, the adjacent angles of a parallelogram are supplementary.

We know that the adjacent angles of a parallelogram are supplementary. So,

(2x – 4)° + (3x – 1)° = 180°

5x – 5° = 180°

5x = 185°

x = `185^circ/5`

x = 37°

So, the adjacent angles are

2x – 4 = 2 × 37° – 4° 

= 74° – 4° 

= 70°

And 3x – 1 = 3 × 37° – 1° 

= 111° – 1° 

= 110°

Hence, the angles are 70°, 110°, 70°, 110°.  ...[Opposite angles in a parallelogram are equal]