in the given figure square ABCD and square PQRC are two parallelogram. if angle A =100° then find the measure of all angles of square PQRC
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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°.
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