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

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In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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New post 20 Aug 2011, 13:56
1
5
00:00
A
B
C
D
E

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  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?

Image

(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
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Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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New post 16 May 2016, 01:26
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u0422811 wrote:
In the figure shown, what is the value of v+x+y+z+w?

Image

(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:
Image
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).

Answer: C.


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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Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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New post 20 Aug 2011, 14:56
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
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Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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New post 20 Aug 2011, 15:10
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
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Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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New post 20 Aug 2011, 15:25
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
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Re: In the figure shown, what is the value of v+x+y+z+w?  [#permalink]

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New post 16 May 2016, 01:05
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.)
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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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