Question

What is m∠PQR?

Answer 1

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°