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Source: — Problem Solving |
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by mevicks » Sun Oct 06, 2013 2:09 am
a = e ... a is the vertically opposite angle of e

Thus we need either of the two to find the answer.

St1:
b + c = 287
b + f = 180 & g + c = 180 ... Supplementary angles

Thus adding the above two: b + f + g + c = 360
But b + c = 287 thus g + c can be found out.
Now in the triangle g + c + e = 180
Thus we can find e. Sufficient.

St2:
by this statement we cannot find either of the two (e or a)
Insufficient.

Answer A
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by GMATGuruNY » Sun Oct 06, 2013 3:59 am
sukhman wrote:Image

What is the degree measure of angle a?
(1) b + c = 287 degrees (2) d + e = 269 degrees[/img]
To evaluate each statement, test TWO combinations of angle measurements
Be sure to satisfy the following constraints:
Angles that form a straight line must add up to 180.
The interior angles of the triangle must add up to 180.

Statement 1: b+c = 287
Case 1:
Image
Here, a = 107.

Case 2:
Image
Here, a = 107.

Since the value of a is the same in each case, SUFFICIENT.

Statement 2: d+e = 269
Case 3:
Image
Here, a = 119.

Case 4:
Image
Here, a = 109.

Since the value of a is NOT the same in each case, INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Sun Oct 06, 2013 7:59 am
sukhman wrote:Image
What is the degree measure of angle a?
(1) b + c = 287 degrees
(2) d + e = 269 degrees
Target question: What is the degree measure of angle a?

Statement 1: b + c = 287 degrees
b + f = 180 [angles on a line add to 180]
c + g = 180 [angles on a line add to 180]
Add equations to get b + c + f + g = 360
Statement 1 tells us that b + c = 287, so we get: 287 + f + g = 360
So, f + g = 73

f + g + e = 180 [angles in triangle add to 180]
So, 73 + e = 180, which means e = 107, which means angle a must be 107 degrees
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: d + e = 269 degrees
There are several triangles that satisfy this condition. Here are two:

Case a:
Brent
Image
Here, angle a = 60 degrees

Case b:
Image
Here, angle a = 70 degrees

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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