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# If a = 25 in the figure above, which of the following statements must

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Math Expert
Joined: 02 Sep 2009
Posts: 54376
If a = 25 in the figure above, which of the following statements must  [#permalink]

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08 Aug 2017, 01:40
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Difficulty:

55% (hard)

Question Stats:

48% (01:23) correct 52% (01:34) wrong based on 72 sessions

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If a = 25 in the figure above, which of the following statements must be true?

I. n is parallel to p
II. q is parallel to r
III. b = 65

(A) None
(B) I only
(C) I and II only
(D) II and III only
(E) I, II and III

Attachment:

2017-08-08_1239.png [ 16.09 KiB | Viewed 1127 times ]

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GPA: 3.57
If a = 25 in the figure above, which of the following statements must  [#permalink]

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Updated on: 10 Aug 2017, 22:19
Bunuel wrote:

If a = 25 in the figure above, which of the following statements must be true?

I. n is parallel to p
II. q is parallel to r
III. b = 65

(A) None
(B) I only
(C) I and II only
(D) II and III only
(E) I, II and III

Attachment:
2017-08-08_1239.png

It should be A

I- For us to conclusively say n and p are parallel, the angles both lines impart on line q need to be proven parallel.
II- Again, we do not know if n and p are parallel so we cannot use their equal angles to suggest q and r are parallel.
III- If line m is perpendicular to q, the internal angles of the triangle would be 90, 65 and $$\angle b = 25$$ (sum of internal angles of a triangle is 180) but we have no evidence that suggests m is perpendicular to q.
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Originally posted by jedit on 08 Aug 2017, 02:28.
Last edited by jedit on 10 Aug 2017, 22:19, edited 1 time in total.
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Re: If a = 25 in the figure above, which of the following statements must  [#permalink]

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10 Aug 2017, 10:54
Bunuel wrote:

If a = 25 in the figure above, which of the following statements must be true?

I. n is parallel to p
II. q is parallel to r
III. b = 65

(A) None
(B) I only
(C) I and II only
(D) II and III only
(E) I, II and III

Attachment:
2017-08-08_1239.png

Since we don’t know the measure of the interior angle of the triangle that also contains angles a and b, there is no way we can determine the measure of angle b, even when we are given angle a = 25. Thus, Roman numeral III is not true. This eliminates answer choices D and E.

Now we are left with statements I and II. Since we need to determine the statement or statements that MUST BE true, let’s see if it’s possible for them not to be true. That is, let’s assume the contrary.

The contrary to statement I is: lines n and p are not parallel. If they are not parallel, then the angle formed by lines p and q that is the corresponding angle to angle a would not be 25 degrees.

The contrary to statement II is: lines q and r are not parallel. If they are not parallel, then the angle formed by lines p and q that is the alternate interior angle to angle a would not be 25 degrees.

We can see that the angle formed by lines p and q in the contrary to statement I is the same angle in the contrary to statement II. Since it is possible that it would not be 25 degrees, it is possible that lines n and p are not parallel and lines q and r are not parallel. Thus, statements I and II don’t have to be true.

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Joined: 07 Jun 2017
Posts: 100
Re: If a = 25 in the figure above, which of the following statements must  [#permalink]

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11 Aug 2017, 08:16
i think i am wrong,, because i thought the upper left triangle would be a right triangle
Re: If a = 25 in the figure above, which of the following statements must   [#permalink] 11 Aug 2017, 08:16
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