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In the figure above, N lies on line segment MO. Which of the following
[#permalink]
24 Aug 2017, 23:54
24 Aug 2017, 23:54
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A
B
C
D
E
Difficulty:
5%
(low)
Question Stats:
95% (01:05) correct
5%
(01:42)
wrong
based on 86
sessions
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
Attachment:
2017-08-25_1042_003.png [ 11.03 KiB | Viewed 2937 times ]
Re: In the figure above, N lies on line segment MO. Which of the following
[#permalink]
25 Aug 2017, 00:20
25 Aug 2017, 00:20
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)
In the figure above, N lies on line segment MO. Which of the following
[#permalink]
25 Aug 2017, 09:56
25 Aug 2017, 09:56
Expert Reply
Bunuel wrote:
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
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 [ 28.9 KiB | Viewed 2386 times ]
