pappueshwar wrote:hi all,
request to assist me in solving the problem :
i feel the answer is C.

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


a /b
--------------------------------------------
c/d


e f
-----------------/----------------------------
g/ h



Sorry for the diagram could not draw better. but its typical two parallel lines cut by a transversal forming 8 angles.

Since the lines are parallel with a transversal
U already know a + f = 180 ( d = a ... and d and f form interior angles..)
U should also notice e = h = a

So ur equations boils down to 180 - a

Hence u need the value of a to find the value of the expression..

Statement 1 doesnt give u anything...
Hence insufficient..

Statement 2 a - f = 180
U already know a + f = 180

hence u can find the value of a from the system of equations and hence the value of your expression..

IMO: B

Hope it helps!!.

It may help here to find the equivalent angles and write them down -
a=d=e=h and c=b=g=f

then write the equation from the question in two variables (using the equivalences)
a+f+a-(a+a) = 2a +f - 2a = f so you are really only looking to solve for the value of f. but with parallel lines you know that any angle from the set containing a plus any angle from the set containing f is 180* - becuase you know any line is 180*.

Statement 1 - gives you info you already know from the definitions so it can't be sufficient leave B/C/E.

Statement 2 tells you that a-f = 60 - since you also knwo that a+f = 180 you have two variables and two equations so you can solve teh problem and thus B is sufficient.