Question

In The following Figure, ABCD and PORS are Parllelogram . Find The value of 'B'
please Help me ​​

Answer 1

Answer:

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