Question

If MN=NQ and MQ=QR=RP, calculate for x​

Answer 1

• C. 18°

Explanation:

• Refer to attached diagram

Given

• MN = NQ
• MQ = QR = RP
• NMR = 3x
• QMR = x

To find

• Value of x

Solution

• MN = NQ ⇒ ∠MRN = ∠QMN = 3x+x = 4x
• MQ = QR ⇒ ∠MRQ = ∠QMR = x

RQP is exterior angle of ΔMQR ⇒

• ∠RQP = x + x = 2x

QR = RP ⇒

• ∠RPQ = ∠RQP = 2x

∠QRN is exterior angle of ΔQRP ⇒

• ∠QRN = 2x + 2x = 4x

• ∠MRN = ∠QRN - ∠QRM = 4x - x = 3x

∠MRN = ∠NMR = 3x ⇒

• NR = MQ

NR = MQ ⇒

• ∠NQR = ∠QRN = 4x

We now have a straight angle MQP:

• ∠MQP = ∠MQN + ∠RQN + ∠RQP
• 180° = 4x + 4x + 2x
• 10x = 180°
• x = 18°

Correct choice is C