Question

the measure of one angle of a parallelogram is 30 degree less than the twice the smallest angle .find the measure of each angel

Answer 1

Let, the measure of smaller angle of parallelogram= x

by given condition,
the measure of bigger angle=2x-30

x+(2x-30)+x+(2x-30)=360
..... [sum of measures of all angles
of parallelogram is 360°]
x+2x-30+x+2x-30=360
x+x+2x+2x-30-30=360
2x+4x-60=360
6x-60=360
6x=360+60
6x=420
x=420/6
x=70

the smaller angle=x=70°
the bigger angle=2x-30
=2(70)-30
=140-30
=110°

Answer 2

Let the smallest angle=x Second angle = 2x-30 Sum of two adjacent angles in a parallelogram=180 x+2x-30=180 3x=180+30 3x=210 x=210/3 x =70 Second angle = 2x-30=2*70-30=110 Therefore Four angles of the parallelogram are 70, 110,70,110