In The following Figure, ABCD and PORS are Parllelogram . Find The value of 'B'
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ABCD & PQRS are parallelogram.
In parallelogram ABCD,
∠A=∠C=100 [opposite angles of parallelogram are equal]
and ∠DCB+∠DCP=180. [Linear pair]
∠DCP=180−100=80 ………..(1)
Now, in parallelogram PQRS,
∠P+∠Q=180 [conjucate angles of parallelogram]
∠SPQ=180−60=120
and ∠SPQ + ∠SPC=180 [linear pair]
∠CSO=180−120=60 ………(2)
Now In ΔCOP
∠COP+∠OCP + ∠CPO=180 [angle sum proportion]
∠COP=180−80−60 [From equation (1) & (2)]
∠COP=40
Hence ∠COP=∠SOD=x=40 (Vertically Opposite Angles)
∠Q = ∠S = 60 [opposite angles of parallelogram are equal]
∠SOD+∠ODS + ∠OSD =180 [angle sum proportion]
40+∠ODS +60 = 180
∠ODS = 180-100
∠ODS = ∠ABC = 80
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