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24 Aug 2017, 23:54
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B
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90% (01:08) correct
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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
Attachment:
2017-08-25_1042_003.png [ 11.03 KiB | Viewed 4165 times ]
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)
25 Aug 2017, 09:56
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Bunuel
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 3468 times ]
