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Line segments AB and CD meet at point C,

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by VJesus12 » Fri Dec 08, 2017 7:06 am
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.
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by GMATWisdom » Fri Dec 08, 2017 10:18 am
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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by [email protected] » Fri Dec 08, 2017 2:35 pm
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...

Answer A: 30 degrees

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.

Final Answer: A

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