What is the value of z in the triangle above?

SOLUTION


What is the value of z in the triangle above?

The interior angles of a triangle always add up to 180°. Thus x+y+z=180°.

(1) x+y=139 --> 139+z=180 --> z=41. Sufficient.

(2) y +z= 108. Cannot determine the value of z. Not sufficient.

Answer: A.
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St 1: Sufficient: x+y=139, therefore Z= 180-139
St 2: Insufficient: y+z=108, the value of x can be found, but we can not get a definite value of z.

Hence Answer A

z = ?
1) z = 180 - (x+y) = 180 - 139 -->Sufficient
2) y+z = 108 --->z can take different values --->Not Sufficient

Answer A

Total measure of the sum of a triangle's interior = 180.

1) x + y + z = 180
139 + z = 180
z = 41 Sufficient

2)x + y + z = 180
x + 108 = 180
x = 72, but we are not sure of the split between y and z, so this is Insufficient

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Answer: A

Z===180-(X+y)
for finding Z we need Sum of X and Y

statement 1: X+Y == given , sufficient
Statement 2; Y+Z ==given , can not find X+y , insufficient


Hence A

Sum of a triangle's interior angles= 180.

1) x + y + z = 180
z = 180 - 139
z = 41.

Hence, A is sufficient to find z.

2) y + z= 108
When we solve the equation we could only find x.

x + y + z = 180
x + 108 = 180
x = 72.

Using the info here we can't find the value of z since we don't know how y and z form 108. so this information is Insufficient

Hence, the answer is A. Only 1 is sufficient.

Hope that helps.


Shower me with Kudos if this helps you understand the problem. :D

(1) x+y=139

180 - 139 = 41 z=41 sufficient


(2) y +z= 108

180 -108 = 72 x= 72 it doesnt give you the value of z

Target question: What is the value of z in the triangle above?
IMPORTANT: Since angles in a triangle must add to 180 degrees, we can write: x + y + z = 180

Statement 1: x + y = 139
Take: x + y + z = 180 and replace (x + y) with 139 to get: 139 + z = 180
Solve equation for z to get: z = 41
So, the answer to the target question is z = 41
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y + z = 108
Take: x + y + z = 180 and replace (y + z) with 108 to get: x + 108 = 180
Solve equation for x to get: x = 72
Hmmm, we know the value of x, but we have no way to find the value of z.
So, statement 2 is NOT SUFFICIENT

If you're not convinced, consider the following scenarios that satisfy statement 2:
Case a: x = 72, y = 50 and z = 58. In this case, the answer to the target question is z = 58
Case b: x = 72, y = 60 and z = 48. In this case, the answer to the target question is z = 48
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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