If MN=NQ and MQ=QR=RP, calculate for x
1 answer:
Answer:
- C. 18°
Step-by-step explanation:
- <em>Refer to attached diagram</em>
- MN = NQ
- MQ = QR = RP
- NMR = 3x
- QMR = x
- Value of x
- MN = NQ ⇒ ∠MRN = ∠QMN = 3x+x = 4x
- MQ = QR ⇒ ∠MRQ = ∠QMR = x
<u>RQP is exterior angle of ΔMQR ⇒ </u>
- ∠RQP = x + x = 2x
<u>QR = RP ⇒ </u>
- ∠RPQ = ∠RQP = 2x
<u>∠QRN is exterior angle of ΔQRP ⇒ </u>
- ∠QRN = 2x + 2x = 4x
- ∠MRN = ∠QRN - ∠QRM = 4x - x = 3x
<u>∠MRN = ∠NMR = 3x ⇒ </u>
- NR = MQ
<u>NR = MQ ⇒ </u>
- ∠NQR = ∠QRN = 4x
<u>We now have a straight angle MQP:</u>
- ∠MQP = ∠MQN + ∠RQN + ∠RQP
- 180° = 4x + 4x + 2x
- 10x = 180°
- x = 18°
Correct choice is C
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