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The measures of two angles of a parallelogram differ by 52 d
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09 May 2015, 10:24
09 May 2015, 10:24
Expert Reply
00:00
Question Stats:
80% (01:31) correct
19% (00:56) wrong based on 46 sessions
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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
Kudos for the right answer and explanation
(A) 38
(B) 52
(C) 64
(D) 76
(E) 128
Kudos for the right answer and explanation
Re: GRE Math Challenge #82-The measures of two angles
[#permalink]
21 Mar 2017, 13:18
21 Mar 2017, 13:18
How to solve this question?
Thanks
Thanks
Re: GRE Math Challenge #82-The measures of two angles
[#permalink]
21 Mar 2017, 16:21
21 Mar 2017, 16:21
Expert Reply
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
quadrilateral-parallelogram.gif [ 1.79 KiB | Viewed 5057 times ]
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
Show: :: image
Attachment:
quadrilateral-parallelogram.gif [ 1.79 KiB | Viewed 5057 times ]
