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

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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 25 Nov 2017, 10:05
In a regular pentagram (5-pointed star, NOT Pentagon), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees.
Attachment:
1.jpg
1.jpg [ 8.1 KiB | Viewed 839 times ]


In an irregular pentagram (NOT Pentagon), the angles might be all different from each other, but the angles in all five points still sum to 180 degrees.
Attachment:
2.jpg
2.jpg [ 17.66 KiB | Viewed 843 times ]

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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 10 Feb 2018, 11:54
Bunuel wrote:
SOLUTION

In the figure shown, what is the value of v+x+y+z+w?
Attachment:
Star.png


(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:
Attachment:
Star2.png
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.


Hi Bunuel,

how can we assume that the shown figure can perfectly be inscribed into a circle. Usually extra assumptions aren't allowed or do I oversee sth.?

Thanks and best regards,
andr3
Re: In the figure shown, what is the value of v+x+y+z+w?   [#permalink] 10 Feb 2018, 11:54

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