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# GRE Math Challenge #82-The measures of two angles

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Joined: 07 Jun 2014
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GRE Math Challenge #82-The measures of two angles [#permalink]  09 May 2015, 10:24
Expert's post
00:00

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
The measures of two angles of a parallelogram differ by 52 degrees. The number of degrees in the smaller angle is

(A) 38
(B) 52
(C) 64
(D) 76
(E) 128
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #82-The measures of two angles [#permalink]  21 Mar 2017, 13:18
How to solve this question?

Thanks
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 107

Kudos [?]: 1833 [0], given: 397

Re: GRE Math Challenge #82-The measures of two angles [#permalink]  21 Mar 2017, 16:21
Expert's post
Explanation

A parallelogram has two angles as seen in image below.

Now we know from the question = $$\angle A - \angle B = 52$$.

And $$\angle A + \angle B + \angle A + \angle B =360$$

Since sum of angles in a quadrilateral. is 360.

$$2 \times (\angle A + \angle B) = 360$$

or $$\angle A + \angle B = 180$$.

Solving for values of $$\angle A$$ and $$\angle B$$.

$$\angle A = 116$$ and $$\angle B = 64$$.

Hence C is correct

[Reveal] Spoiler: image
Attachment:

quadrilateral-parallelogram.gif [ 1.79 KiB | Viewed 1394 times ]

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Re: GRE Math Challenge #82-The measures of two angles   [#permalink] 21 Mar 2017, 16:21
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# GRE Math Challenge #82-The measures of two angles

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