OG - PS - #10 (Diagnostic Test)

by **slsu** Mon Sep 10, 2007 12:43 pm

This question (cannot be drawn), has 5 angles, v,x,y,z, and w, which are all positioned at the points of a star. The question asks for the value of v + x + y + z + w.

Is there a quicker way to solve this problem, aside from the answer cited in the OG guide (which seems a bit lengthy)?

by **StaceyKoprince** Mon Sep 10, 2007 5:22 pm

Please post the exact text of the problem, including answer choices; we do not always have access to our books when answering questions (and, in any event, we would not be able to respond to as many posts if we had to look up every question).

Please also describe any visuals as clearly and completely as you can, if you cannot do a screen shot of the diagram.
Thanks!

by **slsu** Tue Sep 11, 2007 3:42 pm

Here is the question:

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

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

[img]

Is there a quicker way to solve this, aside from what's posted in the OG?[/img]

by **RonPurewal** Fri Sep 14, 2007 6:17 am

There are at least two excellent shortcuts.

(1) Assume symmetry, because nothing implies asymmetry. Make the center pentagon regular; each of its angles is therefore 108 degrees. Then find the triangles' angles explicitly: the ones adjacent to the pentagon are 180 - 108 = 72 degrees each, leaving 180 - 2(72) = 36 degrees for each of the angles you're interested in.

(2) Make a visual estimate (i.e., just guess the angle measures). The answer choices are so far apart that any reasonable estimate for the size of the angles (around 30-40 degrees each) will give an answer much closer to 180 degrees than to any of the wrong answers.