In a quadrilateral PQRS, angle P + angle S = 150° , angle P : angle S = 3:2 and angle Q : angle R = 3:4, Find angles of quadrilateral.
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Correct answer:-
Given
∠P:∠Q:∠R:∠S=3:4:6:7
Let ∠P=3x
∠Q=4x
∠R=6x and
∠S=7x
hence,
∠P+∠Q+∠R+∠S=360
o
3x+4x+6x+7x=360
o
20x=360
o
x=360
o
/20
We get,
x=18
o
So,
∠P=3x=3×18
o
=54
o
∠Q=4x=4×18
o
=72
o
∠R=6x=6×18
o
=108
o
∠S=7x=7×18
o
=126
o
Now adding two adjacent angles, we get
∠Q+∠R=72
o
+108
o
=180
o
and
∠P+∠S=54
o
+126
o
=180
o
Therefore PQ∣∣RS
Since,
∠P+∠Q=54
o
+72
o
=126
o
Which is not equal to 180
o
Therefore, PS and QR are not parallel.
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