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Sub 505 (Easy)|   Geometry|      
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Bunuel
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Line segments AB and CD meet at point C, the midpoint of segment AB. 28 Jul 2017, 00:46
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94% (01:12) correct 6% (01:14) wrong based on 170 sessions

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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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A
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Line segments AB and CD meet at point C, the midpoint of segment AB. 28 Jul 2017, 01:27
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Bunuel
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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AB is a straight line with midpoint C and CD is line segment

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

A
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Line segments AB and CD meet at point C, the midpoint of segment AB. 25 Jul 2020, 05:43
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Bunuel , would you please provide a graphical explanation?
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TestPrepUnlimited
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Line segments AB and CD meet at point C, the midpoint of segment AB. Updated on: 25 Jul 2020, 12:22
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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Bunuel
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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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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Line segments AB and CD meet at point C, the midpoint of segment AB. 25 Jul 2020, 12:22
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msu6800
Bunuel , would you please provide a graphical explanation?
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msu6800 I included a graph in my explanation, hope that helps!
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Line segments AB and CD meet at point C, the midpoint of segment AB. 18 Jun 2023, 18:00
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