ABCD is a parallelogram. Point P and Q are taken on the sides AB and AD, respect

Question

ABCD is a parallelogram. Point P and Q are taken on the sides AB and AD, respectively and the parallelogram PRQA is formed. If

∠ C = 45^{\circ}

, find

∠ R

Answer:
:
Let ABCD be a parallelogram,
where

∠ C = 45^{\circ}

Since, ABCD is a parallelogram,

∠ A = ∠ C

[opposite angles of parallelogram are equal]
Again, since PRQA is a parallelogram,

∠ A = ∠ R

[opposite angles of parallelogram are equal]

\Rightarrow ∠ R = 45^{\circ}

[

∴ ∠ A = ∠ C = 45^{\circ}

]

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