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If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?

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Joined: 02 Sep 2009
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If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?  [#permalink]

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28 Jul 2017, 00:41
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Difficulty:

15% (low)

Question Stats:

100% (00:34) correct 0% (00:00) wrong based on 17 sessions

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If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?

(A) 150°
(B) 140°
(C) 120°
(D) 110°
(E) 100°

Attachment:

2017-07-28_1137_001.png [ 5.23 KiB | Viewed 466 times ]

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Re: If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?  [#permalink]

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28 Jul 2017, 00:44
Bunuel wrote:

If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?

(A) 150°
(B) 140°
(C) 120°
(D) 110°
(E) 100°

Attachment:
2017-07-28_1137_001.png

MQP = 30 => RQM = 60 => RQN = 180-60 =120

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Re: If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?  [#permalink]

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28 Jul 2017, 00:49
Bunuel wrote:

If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?

(A) 150°
(B) 140°
(C) 120°
(D) 110°
(E) 100°

Attachment:
2017-07-28_1137_001.png

$$MN$$ is a straight line.

$$∠PQR = 90°$$

$$∠MQP = 30°$$

$$∠PQR = ∠MQP + ∠MQR$$

$$∠MQR = ∠PQR - ∠MQP = 90° - 30°$$

Therefore ; $$∠MQR = 60°$$

$$∠MQR + ∠RQN = 180°$$

$$∠RQN = 180° - 60° = 120°$$

Re: If MN is a straight line, and ∠MQP = 30°, what is ∠RQN?   [#permalink] 28 Jul 2017, 00:49
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