(1) b + c = 287 degrees
Now, b=180-f and c=180-g, so b+c=180-f+180-g=360-(f+g).
Thus 360-(f+g)=287....f+g=360-287=73
But e+f+g=180....f+g=180-e, so 180-e=73....e=107, and a=e=107
Suff

(2) d + e = 269 degrees
d=180-f , so d + e =180-f+e.Nothing much to find a or e
Insuff

A

This is a Manhattan Question. Below is the OE:

The question asks us to find the degree measure of angle a. Note that a and e are equal since they are vertical angles, so it's also sufficient to find e.

Likewise, you should notice that e + f + g = 180 degrees. Thus, to find e, it is sufficient to find f + g. The question can be rephrased to the following: "What is the value of f + g?"

(1) SUFFICIENT: Statement (1) tells us that b + c = 287 degrees. This information allows us to calculate f + g. More specifically:

b + c = 287
(b + f) + (c + g) = 180 + 180 Two pairs of supplementary angles.
b + c + f + g = 360
287 + f + g = 360
f + g = 73

(2) INSUFFICIENT: Statement (2) tells us that d + e = 269 degrees. Since e = a, this is equivalent to d + a = 269. There are many combinations of d and a that satisfy this constraint, so we cannot determine a unique value for a.

The correct answer is A.

VeritasKarishma plz explain

From the figure, a = e (vertically opposite angles)

Also b = e + g (exterior angle = sum of interior opposite angles)
and c = e + f
and d = e + g

(1) b + c = 287 degrees

This means e + g + e + f = 287
But e + f + g = 180
So e + 180 = 287
e = 107
Sufficient

(2) d + e = 269 degrees
e + g + e = 269
Doesn't help us get e. Not sufficient

Answer (A)
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