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# In a certain Parallelogram the degree measure of one angle exceeds tha

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Senior Manager
Joined: 30 Nov 2010
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Schools: UC Berkley, UCLA
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Kudos [?]: 105 [1] , given: 66

In a certain Parallelogram the degree measure of one angle exceeds tha [#permalink]

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31 Jan 2011, 14:57
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100% (01:38) correct 0% (00:00) wrong based on 7 sessions

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In a certain Parallelogram the degree measure of one angle exceeds that of the other by 30 what is the degree measure of the smaller angle?

75
80
85
90
95
[Reveal] Spoiler: OA

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Re: In a certain Parallelogram the degree measure of one angle exceeds tha [#permalink]

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31 Jan 2011, 15:07
mariyea wrote:
In a certain Parallelogram the degree measure of one angle exceeda that of the other by 30 what is the degree measure of the smaller angle?
75
80
85
90
95

Hi,

parallelograms are composed of two pairs of equal angles (the opposite angles are equal), with each adjacent pair of angles summing to 180 degrees.

So, if we know that:

x + y = 180

and

x - y = 30

We can solve for both angles.

Subtracting the second equation from the first (if we wanted to solve for the bigger angle, we would have added instead of subtracted), we get:

2y = 150

y = 75

choose (A)!
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Re: In a certain Parallelogram the degree measure of one angle exceeds tha [#permalink]

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31 Jan 2011, 15:15
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Expert's post
mariyea wrote:
In a certain Parallelogram the degree measure of one angle exceeda that of the other by 30 what is the degree measure of the smaller angle?
75
80
85
90
95

In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).

Given: x+(x+30)=180 --> x=75.

Check this for more: math-polygons-87336.html
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Schools: UC Berkley, UCLA
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Kudos [?]: 105 [0], given: 66

Re: In a certain Parallelogram the degree measure of one angle exceeds tha [#permalink]

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31 Jan 2011, 15:36
I wasn't aware of that rule. I'll keep that in mind next time. Thank you both!
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Re: In a certain Parallelogram the degree measure of one angle exceeds tha [#permalink]

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01 Feb 2011, 19:48
A

L-S=30

2L + 2S = 180 *2

Solving for S yields S = 75
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Re: In a certain Parallelogram the degree measure of one angle exceeds tha [#permalink]

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07 Feb 2011, 22:31
75
I approached it by the method mentioned above:

although- here is an alternate approach

let x be one angle, the other is x+30

therefore x+ x+30+x+x+30 = 360 summing up all angles

4x +60= 360
x = 75
Re: In a certain Parallelogram the degree measure of one angle exceeds tha   [#permalink] 07 Feb 2011, 22:31
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