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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] New post   16 Jan 2014, 04:52
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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

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Bunuel
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Re: In triangle ABC above, what is x in terms of z ? [#permalink] New post   16 Jan 2014, 04:53
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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 \(x+(37+z)+70=180\) --> \(x=73-z\).

Answer: E.
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Re: In triangle ABC above, what is x in terms of z ? [#permalink] New post   16 Jan 2014, 06:11
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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] New post   16 Jan 2014, 05:33
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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

So E is the answer
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Re: In triangle ABC above, what is x in terms of z ? [#permalink] New post   17 Jan 2014, 00:15
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] New post   25 May 2017, 11:48
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


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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] New post   13 Nov 2017, 03:41
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] New post   01 Dec 2023, 00:48
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