Answer:
1. QS bisects ∠ PQR of Δ PQR.⇒[Given]
2. ∠PQS = 90° [Given]
3.∠PQS =∠RQS ⇒[QS bisects ∠ PQR]
4. .∠PQS +∠RQS =90° [∴∠PQS = 90°⇒given]
2∠PQS =90°⇒ [∠PQS =∠RQS ]
∠PQS=45°
So,∠PQS =∠RQS =45°
2.∠ 2= ∠ 4 [Given]
⇒∠ 2≅ ∠ 4[ congruency postulate]
∠2 and ∠ 3 are supplementary.⇒°[given]
⇒∠2 + ∠ 3=180° [ By the definition of supplementary].........(1)
∠1 and ∠4 are supplementary.⇒[∠1 and ∠4 form linear pair.]
⇒∠1 +∠4=180°[By the definition of supplementary]..............(2)
⇒∠2 + ∠ 3 =∠1 +∠4 [both of them are equal to 180, so they are equal to each other.⇒ Two things equal to same thing are equal to each other[Euclid postulate]]
⇒∠4 +∠3=∠1+∠4 [∠2=∠4⇒(given)]
⇒∠3=∠1 [law of cancellation]
⇒∠3≅∠1 [ Congruency property]
