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# If p, q, and r are the degree measures of the three angles of an isosc

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Joined: 02 Sep 2009
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If p, q, and r are the degree measures of the three angles of an isosc  [#permalink]

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24 Aug 2017, 23:52
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97% (00:35) correct 3% (00:24) wrong based on 49 sessions

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If p, q, and r are the degree measures of the three angles of an isosceles triangle and p = 100, then p – q =

(A) 20
(B) 40
(C) 50
(D) 60
(E) 80

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Re: If p, q, and r are the degree measures of the three angles of an isosc  [#permalink]

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25 Aug 2017, 00:32
If p, q, and r are the degree measures of the three angles
of an isosceles triangle and p = 100, the side opposite to the angle p is unequal.
We cannot a sum of three angles greater than 180.

Let the 2 other angles, q = r = x(opposite to the equal sides)

p + 2x = 180 => 2x = 180 - (p=100)
Therefore q = r = 40 and p – q = 100 - 40 = 60(Option D)
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Re: If p, q, and r are the degree measures of the three angles of an isosc  [#permalink]

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25 Aug 2017, 00:48
Answer should be (D), reverse engineering method solves quick
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Re: If p, q, and r are the degree measures of the three angles of an isosc  [#permalink]

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26 Aug 2017, 19:20
Bunuel wrote:
If p, q, and r are the degree measures of the three angles of an isosceles triangle and p = 100, then p – q =

(A) 20
(B) 40
(C) 50
(D) 60
(E) 80

The sum of angles can't exceed 180. This implies the q= r =40

p - q = 100 - 40 =60

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Re: If p, q, and r are the degree measures of the three angles of an isosc  [#permalink]

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29 Aug 2017, 17:34
Bunuel wrote:
If p, q, and r are the degree measures of the three angles of an isosceles triangle and p = 100, then p – q =

(A) 20
(B) 40
(C) 50
(D) 60
(E) 80

Since a triangle cannot have two interior angles of 100 degrees and since p = 100, the other two angles are equal to each other and they sum to 80 degrees. Therefore, they must be 40 degrees each; thus, p - q = 100 - 40 = 60.

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Re: If p, q, and r are the degree measures of the three angles of an isosc  [#permalink]

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29 Aug 2017, 21:36
The third angle r will be either equal to p or q to be isosceles.
If r=p the sum of angle would exceed 180.
therefore q=r
Solving p + q + r= 180 we get q = r = 40

Hence p - q = 60
Re: If p, q, and r are the degree measures of the three angles of an isosc   [#permalink] 29 Aug 2017, 21:36
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