Question

in the given figure if PQRS is a line , then find the value of x​

Answer 1

Step-by-step explanation:

In parallelogram ABCD,

∠B=∠D=60°(∵Opposite angles in a parallelogram are equal)

Now, in parallelogram PQRS,

∠P+∠S=180°(∵Adjacent angles in a parallelogram are supplementary)

∴∠S=180°−110°=70°

Now,

∠Q=∠S=70°(∵Opposite angles in a parallelogram are equal)

Now, in △BOQ,

∠OBQ+∠OQB+∠BOQ=180°(Angle sum property of a triangle)

∴60°+70°+x=180°

⇒x=180°−130°=50°

Hence the value of x is 50°.