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Manager  Joined: 16 Sep 2010
Posts: 180
Location: United States
Concentration: Finance, Real Estate
GMAT 1: 740 Q48 V42
In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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5 00:00

Difficulty:   45% (medium)

Question Stats: 65% (02:04) correct 35% (01:54) wrong based on 123 sessions

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In the figure shown, what is the value of v+x+y+z+w? (A) 45
(B) 90
(C) 180
(D) 270
(E) 360

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-what-is-the-value-of-v-x-y-z-w-134894.html
Math Expert V
Joined: 02 Sep 2009
Posts: 62496
Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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u0422811 wrote:
In the figure shown, what is the value of v+x+y+z+w? (A) 45
(B) 90
(C) 180
(D) 270
(E) 360

Let's simplify the problem by imagining that we have a star that is inscribed in a circle as shown below: As we can see, 5 arcs subtended by the inscribed angles (x, y, z, w, and v) make the whole circumference. Hence the sum of the corresponding central angles must be 360 degrees, which makes the sum of the inscribed angels 360/2=180 degrees (according to the Central Angle Theorem the measure of inscribed angle is always half the measure of the central angle).

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-what-is-the-value-of-v-x-y-z-w-134894.html
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Manager  Joined: 16 May 2011
Posts: 145
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE: Law (Law)
Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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if it's C then i got the exp like that:
the sum of all angles in the Pentagon are 540(180(n-20))
z+v+ang1(of Pentagon)=180
z+x+ang2=180
w+y+ang3=180
w+x+ang4.=180
x+z+ang5=180
now: 2z+2x+2y+2w+2v+5ang(1,2,3,4,5).=5*180

ang (1,2,3,4,5)=540 as we know that pentagon is ((n-2)*180
2(x+y+z+w+v)+540=900
hence x+y+z+w+v=180
Senior Manager  Joined: 28 Jun 2009
Posts: 344
Location: United States (MA)
Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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I liked this question.

You must be aware of a formula of finding sum of angles of a polygon.
Its (n-2)*180 where n is number of sides the polygon has.

This ways, sum of angles in pentagon = 540.
We have 5 angles. So each angle of 540/5 = 108 degrees.

Now picture the 5 small isosceles angles the star makes at its 5 points.

Let’s take one of that triangle. Say at point x.
Now, x + (180 - 108) + (180 - 108) = 180 ---> 3 points of isosceles triangle.

Solving this x = 36.
And V+X+Y+Z+W = 36*5 = 180
Director  Joined: 01 Feb 2011
Posts: 513
Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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let p,q,r,s ant be the angles of the polygon in the center.

=>p+q+r+s+t = 3(180) = 540 ( as sum of the angles in a polygon with n sides = (n-2)*180 )

then for each of the 5 triangles we will have

x+ 180-p+180-t = 180
y +180-p+180-q = 180
z+180-q+180-r = 180
w+180-r+180-s = 180
v+180-s+180-t = 180

adding all the above 5 equations we have
x+y+z+w+v = 180
Intern  Joined: 06 May 2016
Posts: 14
WE: Education (Education)
Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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Because this is drawn to scale and the answer choices are quite far apart one can quite simply estimate the answer.

(I agree this won't always work but when it does it saves precious time.) Re: In the figure shown, what is the value of v+x+y+z+w?   [#permalink] 16 May 2016, 01:05
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