What is the sum a + b?

Answer is B. 270...
First Found angle a (130) then angle b (140) A+b= 270

sum of interior angles of a shape (n-2)180 where n is the number of sides. For quadrilaterals the sum is 360. thus angle a=140. the adjacent angle is thus 40. b is the sum of the two opposite interior angles thus 90+40 = 130. a+b = 270.

Answer A.

I solved it like this:

right triangle is a 30-60-90 triangle:

Thus at K, angle is 60
for a --> 180 - 60 = 120

for b --> 180 - 30 = 150

together:

270

Answer B

I did not get the same values for a and b as the others. Still, is this way of solving correct?

no the method is wrong because you cannot take the angles as 30-60-90... k is not 60 but 40.
xj and yk are perpendicular on line xyz... so xj and yk are parallel ... which makes angle k = angle j=40(given)...

Hi LaxAvenger,

You've actually come across an interesting "fluke" in the design of this question: the outer triangle is not needed to answer this question. Since the question asks for (A+B) and those two values are on the 'opposite' sides of the two non-90 degree angles, we end up with....

A right triangle, in which the two smaller angles add up to 90....
2 lines which total 360 degrees (of which 90 degrees are already accounted for)....

Under these circumstances, (A+B) will ALWAYS = 270, regardless of what the values of the two smaller triangle angles.

The Official GMAT tends to be a bit more rigorous with its question design though. For example, you might see a similar situation, but the question asks for the value of A-B (which WOULD depend on the the specific values in the entire picture). This is all meant to say that you got a bit "lucky" here.

GMAT assassins aren't born, they're made,
Rich

VERITAS PREP OFFICIAL SOLUTION:

The key to this problem is recognizing the two relationships here that must sum to 180 degrees: the three angles in a triangle must sum to 180, and supplementary angles (those that are formed by splitting a straight line) must also sum to 180. Using those relationships, you should see that:

In the big triangle (JXZ), two angles are already given as 40 and 90, meaning that angle KZY must equal 50, based on the sum of angles in that triangle needing to be 180.

Since that angle KZY is 50, that means that b = 130, as it has to sum with its supplementary angle to 180.

And using the small triangle to the right, KYZ, if you know that the two bottom angles (KYZ and KZY) are 90 and 50, then the third angle (YKZ at the top of that triangle) must account for the remaining 40.

And then since a is supplementary to that 40-degree angle, it has to be 140.

So a = 140 and b = 130, meaning that the sum is 270.

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