an angle of a parallelogram is 20° more than the adjacent angle find the measure of all the angle (sum of adjacent angles of a parallelogram is 180°)
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We know in parallelogram, sum of adjacent angles are supplementary.
∴ x+y=180
o
.
⇒
3
2
y+y=180
o
[ From ( 1 ) ]
⇒ 2y+3y=540
o
⇒ 5y=540
o
⇒ y=108
o
.
Substituting value of y in equation ( 1 ) we get,
⇒ x=
3
2
×108
o
⇒ x=72
o
We know that, in parallelogram opposite angles are equal.
∴ Four angles of parallelogram are 108
o
,72
o
,108
o
and 72
o
.
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