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The ratio of the adjacent angles of a parallelogram is 7 : 8

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The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post Updated on: 14 Mar 2013, 06:18
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The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?

(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these

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Originally posted by ratan19 on 14 Mar 2013, 05:18.
Last edited by Bunuel on 14 Mar 2013, 06:18, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 14 Mar 2013, 06:27
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ratan19 wrote:
The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?

(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these


The adjacent angles of a parallelogram are supplementary (supplementary angles are two angles that add up to 180°), so we have that 7x+8x=180° --> x=12 --> the smaller angle of the parallelogram is 7x=84°.

Next, the sum of interior angles of a polygon is 180(n-2) where n is the number of sides (so is the number of angles). So, the sum of the interior angles of any quadrilateral is 180*2=360°. So, we have that 5y+6y+7y+12y=360° --> y=12° --> the second largest angle of the quadrilateral is 7y=84°.

The sum = 84°+84°=168°.

Answer: A.

For more on polygons check Polygons chapter of Math Book: math-polygons-87336.html

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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 14 Mar 2013, 06:30
Thank you very much, Bunuel!
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 11 Apr 2013, 06:40
Pls suggest , why we haven't added 5 y ( 5 *12) + 7 y ( 7*12) = 144...
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 11 Apr 2013, 06:49
targetbschool wrote:
Pls suggest , why we haven't added 5 y ( 5 *12) + 7 y ( 7*12) = 144...


Read the question carefully:
"What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?"
smaller angle of the parallelogram=7*12°=84°.
second largest angle of the quadrilateral=7*12°=84°.
84°+84°=168°
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 11 Apr 2013, 06:52
oops... My bad :( ...

Thanks for prompt reply..
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The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 10 May 2016, 09:08
ratan19 wrote:
The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?

(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these


The measures of the adjacent angles of a parallelogram add up to be 180°

Given

Quote:
The ratio of the adjacent angles of a parallelogram is 7 : 8


So, 7x + 8x = 180°

Or, 15x = 180°

Or, x = 12°

Hence the angles of the parallelogram are 84° and 96°

Further it is given

Quote:
ratio of the angles of quadrilateral is 5 : 6 : 7 : 12


We know sum of all the four angles of a quadrilateral is 360°

So, 5y + 6y + 7y + 12 y = 360°

Or, 5y + 6y + 7y + 12 y = 360°

Or, 30y = 360°

Or, y = 12°

Hence the angles of the quadrilateral are 60° , 72, 84° and 144°

Quote:
sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral


Will be 84° + 84° = 168°

Hence correct answer will be (A) 168° :-D :P
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 10 May 2016, 11:58
Sum of adjacent angles of parallelogram is 180
7x+8x= 180
x= 12
Smallest angle = 12*7------1

Sum of all angles of a Quadrilateral is 360
5y+6y+7y+12y= 360
y=12
2nd largest angle= 7*12-----2

Sum of equation 1 and 2
2*12*7= 168

'A' is the answer
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 06 Jun 2016, 13:34
Adjacent angles of a parallelogram are supplementary (their total is \(180^{\circ}\))
consider common ratio for angles of parallelogram as x
7x + 8x = 180
15x = 180
x = 12
so smaller of the 2 angles is 7x = 7 * 12 =\(84^{\circ}\)

sum of all angles of a quadrilateral is \(360^{\circ}\)
consider common ratio for angles of quadrilateral as y
5y + 6y + 7y + 12y = 360
30y = 360
y = 12
second largest angle of the quadrilateral is 7x = 7 * 12 =\(84^{\circ}\)

sum of smaller of the 2 angles of parallelogram and second largest angle of the quadrilateral is 84 +84 = \(168^{\circ}\)
Correct Answer - A
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8  [#permalink]

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New post 02 Jul 2017, 00:24
only thing we need to keep in mind is the question is talking about two entities: parallelogram n quadrilateral. once this is clear, we can easily find out all the angles.

answer is A
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Re: The ratio of the adjacent angles of a parallelogram is 7 : 8   [#permalink] 02 Jul 2017, 00:24
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