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

If MN=NQ and MQ=QR=RP, calculate for x​-example-1
User Hamobi
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1 Answer

9 votes
9 votes

Answer:

  • 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

If MN=NQ and MQ=QR=RP, calculate for x​-example-1
User Peter Constable
by
3.1k points