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In the figure above, N lies on line segment MO. Which of the following

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In the figure above, N lies on line segment MO. Which of the following [#permalink]

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New post 24 Aug 2017, 23:54
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In the figure above, N lies on line segment MO. Which of the following gives y in terms of x?

(A) 2x
(B) 2x + 5
(C) 3x + 5
(D) 90 –x
(E) 180 – 3x

[Reveal] Spoiler:
Attachment:
2017-08-25_1042_003.png
2017-08-25_1042_003.png [ 11.03 KiB | Viewed 1303 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, N lies on line segment MO. Which of the following [#permalink]

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New post 25 Aug 2017, 00:20
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The third angle formed in the triangle is 180 - x - y
because angles in a straight line sum up to 180.

The sum of three angles in a triangle, also sum up to 180.
180 - x - y + 2x + x + 5 = 180
2x + 5 - y = 0

Since we have been asked to find the value of y in terms of x,
we get y = 2x + 5(Option B)
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In the figure above, N lies on line segment MO. Which of the following [#permalink]

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New post 25 Aug 2017, 09:56
Bunuel wrote:
Image
In the figure above, N lies on line segment MO. Which of the following gives y in terms of x?

(A) 2x
(B) 2x + 5
(C) 3x + 5
(D) 90 –x
(E) 180 – 3x

[Reveal] Spoiler:
Attachment:
The attachment 2017-08-25_1042_003.png is no longer available

Sometimes, in problems such as this one with many letters (vertices and variables), the written solution can be hard to follow. Hence diagram below.

Solve for y in terms of x by using the properties of exterior angles.

1. Exterior angle: Angle ONQ is an exterior angle whose measure is the sum of non-adjacent interior angles M and Q

∠ M + ∠ Q = ∠ ONQ

2. Given:

∠ M = 2x
∠ Q = x + 5
∠ ONQ = x + y

3. Equation and solution

∠ M + ∠ Q = ∠ ONQ

2x + (x + 5) = x + y

3x + 5 = x + y

2x + 5 = y

Answer B
Attachment:
exteriorangle.png
exteriorangle.png [ 28.9 KiB | Viewed 904 times ]

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Re: In the figure above, N lies on line segment MO. Which of the following [#permalink]

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New post 26 Aug 2017, 19:29
Bunuel wrote:
Image
In the figure above, N lies on line segment MO. Which of the following gives y in terms of x?

(A) 2x
(B) 2x + 5
(C) 3x + 5
(D) 90 –x
(E) 180 – 3x

[Reveal] Spoiler:
Attachment:
2017-08-25_1042_003.png



Let x = 30...........then2x = 60 & x + 5 = 35 & ∠ MNQ = 85

Therefore y = 180 - 85 -30 =65

Substitute in each choice

(A) 2x = 60.....................Eliminate

(B) 2x + 5 = 65...............Keep

(C) 3x + 5 = 95...............Eliminate

(D) 90 –x = 60................Eliminate

(E) 180 – 3x = 90 ...........Eliminate

Answer: B

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Re: In the figure above, N lies on line segment MO. Which of the following [#permalink]

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New post 29 Aug 2017, 06:20
Exterior angle x+y = the sum of the interior opposite angles. Therefore, x+y = 3x + 5.
Y= 2x+5

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Re: In the figure above, N lies on line segment MO. Which of the following [#permalink]

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New post 29 Aug 2017, 17:26
Bunuel wrote:
Image
In the figure above, N lies on line segment MO. Which of the following gives y in terms of x?

(A) 2x
(B) 2x + 5
(C) 3x + 5
(D) 90 –x
(E) 180 – 3x

[Reveal] Spoiler:
Attachment:
2017-08-25_1042_003.png

We see that angle ONQ is an exterior angle of triangle NMQ, meaning that it is remote to the two interior angles M and Q. Since the measure of an exterior angle of a triangle is the sum of the measures of the two remote interior angles, we have:

x + y = 2x + (x + 5)

x + y = 3x + 5

y = 2x + 5

Answer: B
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Re: In the figure above, N lies on line segment MO. Which of the following   [#permalink] 29 Aug 2017, 17:26
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