D10 OG 12 Page 21 Geometry

[EMAN]

In the figure shown, what is the value of v + x + y + x + w?

(A)45
(B)90
(C)180
(D)270
(E)360


(In the book there is a diagram of an uneven five pointed star with the bottom of the points having lines close them off. In other words, if you drew a star by hand with all the crossing lines, that's essentially what it looks like. Starting at 12:00 and going clockwise, it goes y, z, w, v, and x in degrees at each triangular point).

The OG explanation makes sense but it's very tedious in that you have to first use the formula (5-2) x 180 = 540. Then you have to find five separate triangles in the diagram that add up to the answer. With all this information, there's some substitution and factoring to get to the answer. There has to be an easier way to approach this problem. Please advise.

[GMATBootcamp]

I would just visually estimate, since the answer choices are all fairly spread out.

If you start by looking at the triangle formed by angle x and z, the third angle is slightly larger than 90 degrees. I would approximate and just say it is 100. Angles x + z is then equal to 180 - 100 = 80.

I would divide 80 by 2 to find the average angle between x and z, which is 40. Use 40 as the benchmark for the average angle measure of each point on the star.

5 x 40 = 200, which is closest to 180. So I would select answer C


Hope that helps!