Question 180
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 $∠ R$ .

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Solution

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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Question 180 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∘, find ∠R.

Let ABCD be a parallelogram, where ∠C=45∘ 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] ⇒∠R=45∘ [∴∠A=∠C=45∘]

Question 180
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 $∠ R$ .