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In the figure above, if RSTU is a rectangle, what is the val [#permalink]
Expert's post 00:00

Question Stats: 84% (01:09) correct 16% (02:20) wrong based on 25 sessions

Attachment: #GREpracticequestion In the figure above, if RSTU is a rectangle, what is the value of a + b + c + d + e + f.jpg [ 12.02 KiB | Viewed 891 times ]

In the figure above, if RSTU is a rectangle, what is the value of a + b + c + d + e + f ?

[Reveal] Spoiler: OA
270

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Director Joined: 03 Sep 2017
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Re: In the figure above, if RSTU is a rectangle, what is the val [#permalink]
The sum of all these angles is (180°+180°+90°)-(180°) = 270°. The explanation is that a and f are part of a 90 degree angle, while b,c and d,e are part of 180° angles. To all of them is subtracted an angle belonging to a triangle, whose angles sum to 180°. Director Joined: 20 Apr 2016
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Re: In the figure above, if RSTU is a rectangle, what is the val [#permalink]
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Carcass wrote:

In the figure above, if RSTU is a rectangle, what is the value of a + b + c + d + e + f ?

[Reveal] Spoiler: OA
270

We know in rectangle all angles are equal to 90 degree i.e angle r = angle s = angle t =angle u = 90 degree.

Now consider triangle RSX,

We have angle a + angle s +angle b = 180 degree

or angle a +angle b = 90 (since angle s = 90 degree)

Similarly in triangle XYT we have

angle c + angle d + angle t =180 degree

or angle c + angle d = 90 (since angle t = 90 degree)

and in triangle YRU

we have angle e +angle f + angle u =180 degree

or angle e + angle f =90 (since angle u = 90 degree)

Now putting the values in we get (a+b) +(c+d) + (e+f) = 90+90+90 = 270
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Re: In the figure above, if RSTU is a rectangle, what is the val [#permalink]
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Triangle RSX: Angle S=90, hence Angle A+B=90
TRiangle XTY: Angle T=90, hence Angle c+d=90
Triangle YUR: Angle U=90, hence Angle e+f=90

A+B+C+D+E+F=90+90+90=270 Re: In the figure above, if RSTU is a rectangle, what is the val   [#permalink] 06 Feb 2019, 14:25
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