in a quadilateral pqrs PQ Parallel to SR ∠ S:Angle R=5:4 and angle q= 72 find angle p +angle r
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Ratios of angles are 3:4:5:6
Let the angles be P=3x,Q=4x,R=5x and S=6x.
Sum of angles of the quadrilateral is 360
o
.
∴ 3x+4x+5x+6x=360
o
⇒ 18x=360
o
⇒ x=
18
360
o
⇒ x=20
o
⇒ ∠P=3x=3×20
o
=60
o
⇒ ∠Q=4x=4×20
o
=80
o
⇒ ∠R=5x=5×20
o
=100
o
⇒ ∠S=6x=6×20
o
=120
o
⇒ ∠P+∠S=60
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+120
o
=180
o
⇒ ∠Q+∠R=80
o
+100
o
=180
o
∴ PQ∥RS
Since, one pair of quadrilateral is parallel then, it is trapezium.
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