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# Line segments AB and CD meet at point C,

tagged by: VJesus12

### Top Member

#### Line segments AB and CD meet at point C,

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 OA is A.

I know that option C, D and E are incorrect. But how can I know what is the correct option between A and B? Experts, I need your help here please.

### GMAT/MBA Expert

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Posted:
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Hi VJesus12,

We're told that 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° and one of the angles is 5 TIMES as large as the other. We're asked for the degree measure of the SMALLER angle. This question can be solved by TESTing THE ANSWERS.

The 2 angles described in the prompt essentially split the line into 2 pieces - and the SUM of those 2 angles will be 180 degrees. We know the larger angle is 5 TIMES the smaller angle, so let's start with Answer A and see what the larger angle (and total) would be...

IF....
the smaller angle is 30 degrees...
then the larger angle is 5(30) = 150 degrees
30 + 150 = 180 degrees - and that fits everything that we're told, so this must be the answer.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

Master | Next Rank: 500 Posts
Joined
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Posted:
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VJesus12 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 OA is A.

I know that option C, D and E are incorrect. But how can I know what is the correct option between A and B? Experts, I need your help here please.
sum of both the angles formed is 180

this has to be divided into 1 : 5

so one angle would be 180/6 = 30

and the other angle would be 180-30 = 150

measure of smaller angle = 30

hence A is correct option

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