Question

The difference between the two adjacent angles of a parallelogram is 20°. Find measures of all the angles of the parallelogram.

Answer 1

let the angles be x and x-20
the sum of adjacent angles of a paralleogram is 180°
so
x+(x-20)=180°
x+x-20=180°
2x-20=180°
2x=180+20
2x=200
x=200/2
x=100

so the adjacent angles will be
x=100°
The opposite angle to x will be of measure 100°

and the other angle will be
x-20
=100-20
=80°
the opposite angle opposite to angle (x-20)
will be 80°.

verifying our answer :-

sum of adjacent angles =180°
100°+80°=180°
180°=180°


sum of all angles =360°
2(80)+2(100)=360°
160+200=360°
360°=360°