Answer: (B)
(2) alone is sufficient.

Let's consider these one-by-one:

(1) a+f = 180

This does not provide any information we don't already have. If the lines are parallel, the following equalities hold -
a = d (opposite angles)
a = e (corresponding angles)
b + d = 180
a + b = 180
e + f = 180
d + f = 180
b = f and so on.

So, we already know that a + f = 180.

This is not helpful in finding (a + f + d) – (e + h), as we don't know any of these values.

(2) a - f = 60

This is SUFFICIENT:

a + f = 180 (because a = d and d+f = 180, which is because d + b = 180 and b = f)
a - f = 60

So, 2a = 240

or a = 120

Also, a = d so d = 120; f = 180 - a = 60 ; e = a = 120 ; h = e = 120

So, we can evaluate (a + f + d) – (e + h).

Hence sufficient.


Answer: (B)
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If the two horizontal lines in the figure provided are parallel, what is (a + f + d) – (e + h)?

(1) a + f = 180

(2) a – f = 60

answer (B)
(a + f + d) – (e + h)?
a=e & d=h ( corresponding angles)

so a+f+d-a-d=f
To find f, we need two equations but we know that a+f=180
So we only need a-f=60

The question stem says the horizontal lines are parallel.

Using this information we can deduce,
a = d -------------------(1) (opposite angles)

a= e ------------------(2) (corresponding angles)

e= h ------------------(3) (opposite angles) , therefore a = h

d + f = 180
from (1)
a + f = 180 ----------- (4)

using this info in the equation (a + f + d) – (e + h)

180 + a - 2a => 180 - a --------------- (5)

Statement 1:

a + f = 180 => same as eq. (4) . No new info. Cannot get the value - Insufficient

statement 2

a – f = 60 ------------- (6)
from (4) and (6) can find the value of a
substitute in (5) we can find the value of (a + f + d) – (e + h)

Ans B => Statement 2 sufficient

Given : From Parallel Line case,
a = d = e = h
b = c = f = g

Question : what is (a + f + d) – (e + h) = (a+f+a) - (a+a) = f = ?

Statement 1: a + f = 180
a is Unknown Hence f can't be calculated
Also, a+f=180 is a Universal Truth (Supplementary angles) and no extra information so this can't be used to answer the question because we are expected to know about this information
NOT SUFFICIENT

Statement 2: a - f = 60
Also, We know a+f=180 (Supplementary angles)
i.e. a = 120 and f = 60
SUFFICIENT

Answer: option B
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Remember equal number of variables and independent equations ensures a solution.

If the two horizontal lines in the figure provided are parallel, what is (a + f + d) – (e + h)?

(1) a + f = 180

(2) a – f = 60

Transforming the original condition and the question, we have a=d=e=h thus (a + f + d) – (e + h)?--> f=?. a+f=180 we have 2 variables (a,f), and 1 equation (a+f=180) therefore we need 1 more equation. Therefore there is high probability that D is the answer

In case of 1), a+f=180 is the repetition of the original condition. Therefore the condition is not sufficient.
In case of 2), a-f=60 and a+f=180 gives us 2f=120, f=60. Therefore the condition is sufficient, and the answer is B.

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A + B = 180
B = F
A + F = 180
Therefore you should skip this option first of all