There's a useful GMAT-specific logical principle that can be applied here. Notice that this question has 5 exact numerical answer choices; we don't have an answer which says 'cannot be determined'. Well, a GMAT question can't have more than one right answer. So if one of those five answers is right, it must be right no matter how we choose to draw the diagram. Whether the diagram is drawn in some skew way, or completely symmetrically, the answer must always be the same, or they couldn't ask the question this way to begin with. If the answer were different depending how you drew the picture, they'd need an answer choice which said "cannot be determined".

So we're free to just draw the most symmetric diagram possible and solve the question using that. So we can make the middle pentagon a regular pentagon, so each angle is 540/5 = 108 degrees. Then the exterior triangles become isosceles, with angles 72-72-36, where the angles at each point of the star are 36 degrees. Since we need to sum the angles at the five points, the answer is 5*36 = 180.

It's a much longer problem if one answer choice does say "cannot be determined", since then you actually have to prove the answer is the same even when the diagram is drawn in some irregular way.

Hi All,

To start, it’s incredibly rare to see a Quant question on the GMAT with so many inter-connected shapes (including a hexagon!), so you shouldn’t worry about this question if you got it wrong the first time you attempted it. You can solve it with a mix of Geometry rules and TESTing VALUES.

With geometric shapes, every time you “add a side”, you increase the total number of degrees by 180. For example….

A triangle = 180 degrees
A square/rectangle = 360 degrees
A hexagon (5-sided shape) = 540 degrees
Etc.

Since we are not given any information about any of the angles in this picture, we can TEST VALUES. Since the hexagon includes 5 angles that total 540 degrees, it’s easiest to make all 5 angles the same…. 540/5 = 108 degrees each.

The sum of the angles on a line add up to 180 degrees, so each angle in each of the triangles that is next to a 108 degree hexagon angle is equal to 72.

That means that each triangle is an isosceles triangle with two 72 degree angles and one angle that equals… 180 – 72 – 72 = 36 degrees. Thus, V = W = X = Y = Z = 36 and the sum of those 5 angles is (5)(36) = 180 degrees.

Final Answer: C

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