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# In triangle ABC above, what is x in terms of z ?

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In triangle ABC above, what is x in terms of z ? [#permalink]

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16 Jan 2014, 03:52
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:

Untitled.png [ 15.2 KiB | Viewed 9011 times ]
In triangle ABC above, what is x in terms of z ?

(A) z + 73
(B) z -73
(C) 70 - z
(B) z - 70
(E) 73 - z

Problem Solving
Question: 44
Category: Geometry Angle measure in degrees
Page: 67
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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[Reveal] Spoiler: OA

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Re: In triangle ABC above, what is x in terms of z ? [#permalink]

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16 Jan 2014, 03:53
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SOLUTION

In triangle ABC above, what is x in terms of z ?

(A) z + 73
(B) z -73
(C) 70 - z
(B) z - 70
(E) 73 - z

The sum of the degree measures of the angles in a triangle equals 180°, thus we have that $$x+(37+z)+70=180$$ --> $$x=73-z$$.

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Re: In triangle ABC above, what is x in terms of z ? [#permalink]

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16 Jan 2014, 04:33
We know that the sum of internal angles in a triangle is 180 so:
70+37+z+x = 180
Putting in terms of X we have
107-180+z=-x
-73+z=-x Multiplying all the equation for -1
73-z=x

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Re: In triangle ABC above, what is x in terms of z ? [#permalink]

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16 Jan 2014, 05:11
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[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In triangle ABC above, what is x in terms of z ?

(A) z + 73
(B) z -73
(C) 70 - z
(B) z - 70
(E) 73 - z

Let us say z = 13 degrees.

x + 70 + 50 = 180
x = 60 degrees

By plugging in z = 13 we should get answer as 60 degrees which is answer option E.
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Re: In triangle ABC above, what is x in terms of z ? [#permalink]

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16 Jan 2014, 23:15
By the theory of sum of all angles in a triangle being 180 degrees,
angle A + angle B + angle C = 180;
x + (37+z) + 70 = 180;
x + z = 180 - 107;
x + z = 73;
x = 73 - z;

Ans is (E).

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Re: In triangle ABC above, what is x in terms of z ? [#permalink]

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25 May 2017, 10:48
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In triangle ABC above, what is x in terms of z ?

(A) z + 73
(B) z -73
(C) 70 - z
(B) z - 70
(E) 73 - z

Problem Solving
Question: 44
Category: Geometry Angle measure in degrees
Page: 67
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

It's best to work until you find a supplementary relationship between the two. The unlabeled angle in the triangle with x = 180 - 37 - x or 143 -x. Meanwhile, the supplementary angle for the "z" triangle is 180 - z - 70 = 110-z

110-z + 143 - x = 180 because they are on the same line.

So 143 - x - z = 70
-x - z = -73

x = 73 - z

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Re: In triangle ABC above, what is x in terms of z ? [#permalink]

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13 Nov 2017, 02:41
We can solve this question using the angle sum formula (x+37+z+70= 180) or external angle formula (180-(x+37)= z+70).
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Re: In triangle ABC above, what is x in terms of z ?   [#permalink] 13 Nov 2017, 02:41
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