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Line segments AB and CD meet at point C, the midpoint of segment AB.

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Bunuel
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Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink] New post   28 Jul 2017, 00:46
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Line segments AB and CD meet at point C, the midpoint of segment AB. There are two angles formed, each of whose measures is less than 180°. If one of the angles is 5 times as large as the other, what is the degree measure of the smaller angle?

(A) 30
(B) 36
(C) 144
(D) 150
(E) 180
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TestPrepUnlimited
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Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink] New post   Updated on: 25 Jul 2020, 12:22
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Bunuel wrote:
Line segments AB and CD meet at point C, the midpoint of segment AB. There are two angles formed, each of whose measures is less than 180°. If one of the angles is 5 times as large as the other, what is the degree measure of the smaller angle?

(A) 30
(B) 36
(C) 144
(D) 150
(E) 180


The two angles formed add up to 180. A nice shortcut is to pretend you have 5 chunks and 1 chunk, then in total you have 6 chunks and in this case 6 chunk add up to 180 degrees. Then in your head you can find one chunk is worth 30 degrees, the bigger angle would be 5 * 30 = 150.

Note however having C in the midpoint was not useful information, C can be anywhere between A and B.

Ans: A
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Originally posted by TestPrepUnlimited on 25 Jul 2020, 12:21.
Last edited by TestPrepUnlimited on 25 Jul 2020, 12:22, edited 1 time in total.
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Luckisnoexcuse
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Re: Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink] New post   28 Jul 2017, 01:27
Bunuel wrote:
Line segments AB and CD meet at point C, the midpoint of segment AB. There are two angles formed, each of whose measures is less than 180°. If one of the angles is 5 times as large as the other, what is the degree measure of the smaller angle?

(A) 30
(B) 36
(C) 144
(D) 150
(E) 180


AB is a straight line with midpoint C and CD is line segment

Now ACD + BCD = 180
6x = 180
x = 30

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Re: Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink] New post   25 Jul 2020, 05:43
Bunuel , would you please provide a graphical explanation?
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Re: Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink] New post   25 Jul 2020, 12:22
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msu6800 wrote:
Bunuel , would you please provide a graphical explanation?


msu6800 I included a graph in my explanation, hope that helps!
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Re: Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink] New post   18 Jun 2023, 18:00
Hello from the GMAT Club BumpBot!

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Re: Line segments AB and CD meet at point C, the midpoint of segment AB. [#permalink]
18 Jun 2023, 18:00
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