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# The measures of two angles of a parallelogram differ by 52 degrees. Th

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Math Expert
Joined: 02 Sep 2009
Posts: 51223
The measures of two angles of a parallelogram differ by 52 degrees. Th  [#permalink]

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12 Jul 2018, 23:11
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:28) correct 31% (01:41) wrong based on 26 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

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Posts: 931
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Re: The measures of two angles of a parallelogram differ by 52 degrees. Th  [#permalink]

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12 Jul 2018, 23:21
Bunuel wrote:
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

Let x and y are the measure two adjacent angles of the parallelogram, So the measure of the 4 angles of parallelogram are x,y,x, and y in cyclic order.

Given x-y=52 degree----(1)

We know, sum of adjacent angles in a parallelogram is 180.
So, x+y=180.------(2)

Solving (1) & (2) , we have

x=116 degree & y=64 degree.

So, the measure of smallest angle is 64 degree.

Ans. (C)
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Re: The measures of two angles of a parallelogram differ by 52 degrees. Th  [#permalink]

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12 Jul 2018, 23:21
Bunuel wrote:
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

Let, the angles be a and b
a + a+ b+ b = 360
a + b = 180 --> (1)

Given,
a - b = 52 --> (2)

Solving (1) and (2), we get a = 116 (larger)
b = 64 (smaller)

Hence, C.
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Joined: 14 Jun 2018
Posts: 222
Re: The measures of two angles of a parallelogram differ by 52 degrees. Th  [#permalink]

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12 Jul 2018, 23:33
Let the larger angle be x.
In a parallelogram , opposite sides are congruent.
So we have , 2x + 2(x-52) = 360 ; x= 116 and x-52 = 64.
Option C
Re: The measures of two angles of a parallelogram differ by 52 degrees. Th &nbs [#permalink] 12 Jul 2018, 23:33
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