Question

If in the given figure ABCD and feet PQRS are parallelogram, then the value of x
is​

Answer 1

Answer:

ABCD & PQRS are parallelogram.

In parallelogram ABCD,

∠A=∠C=120

o

[opposite angles of parallelogram are equal]

and ∠DCB+∠SCO=180. [Linear pair]

∠SCO=180−120=60 ………..(1)

Now, in parallelogram PQRS,

∠S+∠R=180

o

[conjucate angles of parallelogram]

∠RSP=180−50=130

and ∠RSP+∠CSO=180 [linear pair]

∠CSO=180−130=50

o

………(2)

Now In ΔCOS

∠COS+∠OCS+∠CSO=180

o

[angle sum proportion]

∠COS=180−50−60 [From equation (1) & (2)]

∠COS=70

o

Hence ∠COS=∠POB=x=70

o

[vertically opposite angles]

Therefore value of x is 70

o

.

Answer 2

x=50

angle R=70

i.e angle Q =70....angles in linear pair

angle A=120

• i.e angle D =60
• there for angle c =60
• angle Q=70
• anglec=60
• angle c+Q+x=180....sum of measure of all angles of the triangle is 180
• c=60
• Q=70
• 60+70+anglex=180
• x=180-130
• X=50