In the following figure, ABCD is a parallelogram.If $∠ A B P = x ∠ C B P$ ,then find the value of $x$ .

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Solution

From the figure
$A D = D P = C P = B C$
In $△ P C B,$
$C P = B C ⟹ ∠ C P B = ∠ C B P$
$P C ∥ A B ⟹ ∠ C P B = ∠ A B P$
$⟹ ∠ A B P = ∠ C B P ⟹ x = 1$

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