Question

please answer it i beg you ;-;​

Answer 1

Answer:

In parallelogram ABCD,

∠A=∠C=120

o

[opposite angles of a parallelogram are equal]

and ∠DCB+∠SCO=180

∘

[Linear pair]

∠SCO=180−120=60

∘

...(1)

Now, in parallelogram PQRS,

∠S+∠R=180

∘

[adjacent angles of parallelogram]

∠RSP=180−50=130

∘

and ∠RSP+∠CSO=180

∘

[linear pair]

∠CSO=180−130=50

∘

...(2)

Now In ΔCOS,

∠COS+∠OCS+∠CSO=180

∘

[angle sum proportion]

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

∠COS=70

∘

Hence ∠COS=∠POB [vertically opposite angles]

⇒x=70

∘

Therefore the value of x is 70

∘.

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Answer 2

Solution:

Since ABCD is a parallelogram

agl(DAB) + agl(ABC) = 180°

agl(ABC) = 180° - 130° = 50°

Since PQRS is a parallelogram

agl(SRQ) = agl(SPQ) = 30°

Now

in triangle PBO(let)

agl(P) + agl(B) + x = 180°

30° + 50° + x = 180°

x = 180° - 80° = 100°

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