Answer: m∠PQR = 134°
Step-by-step explanation:
Given: PS is line segment. Q is the point between segment PS. QR is another line segment passes through segment PS.
That means ∠PQR and ∠SQR are linear pair [Linear pair is a pair of two angles made on one line and their sum is 180°]
⇒ ∠PQR + ∠SQR = 180° (i)
Since, ∠PQR is (3x + 5)° and ∠ SQR is (x + 3)° [given]
Put this in (i), we get
(3x + 5)° + (x + 3)° = 180°
⇒ 3x + 5 + x + 3 = 180
⇒ 4 x + 8 = 180
⇒ 4 x = 180-8
⇒ 4 x = 172
Divide both sides by 4
⇒ x= 43
So, ∠PQR= (3(43) + 5)° = 134°
Hence, m∠PQR = 134°
