If an angle of parallelogram is 2/3 of its adjacent angle , the smallest and largest angle will be respectively (in degree)
60,120
80,100
72,108
62,118
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If an angle of a parallelog...
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If an angle of a parallelogram is two-third of its adjacent angle, find all the four angles.
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Let x and y be two adjacent angles of a parallelogram.
According to the question,
⇒ x=
3
2
y ----- ( 1 )
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 angle
∴ Four angles of parallelogram are 108
o
,72
o
,108
o
and 72
o
.
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