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In the figure above a + b + f =
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07 May 2020, 06:13
07 May 2020, 06:13
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#greprepclub In the figure above a + b + f =.jpg [ 19.83 KiB | Viewed 2917 times ]
In the figure above a + b + f =
A. 180 + (c + d + e)
B. 360 − (c + d + e)
C. 360 + (c + d – e)
D. 540 − (c + d+ e)
E. 540 − (c + d – e)
Kudos for the right answer and explanation
Re: In the figure above a + b + f =
[#permalink]
07 May 2020, 06:43
07 May 2020, 06:43
2
a+b+c = 360
a+b = 360-c
c+f+90+90 = 360
f = 180 - c
a+b+f = 540 -2c
Considering the whole triangle
e+d+f = 180
f = 180-(e+d)
180-c = 180 - (e+d)
c = (e+d) --------(1)
a+b+f = 540-(c+c)
a+b+f = 540-(c+e+d) [Using (1)]
Hence option (D)
a+b = 360-c
c+f+90+90 = 360
f = 180 - c
a+b+f = 540 -2c
Considering the whole triangle
e+d+f = 180
f = 180-(e+d)
180-c = 180 - (e+d)
c = (e+d) --------(1)
a+b+f = 540-(c+c)
a+b+f = 540-(c+e+d) [Using (1)]
Hence option (D)
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Joined: 30 Aug 2020
Posts: 23
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GRE 1: Q165 V170
Re: In the figure above a + b + f =
[#permalink]
09 Oct 2020, 02:10
09 Oct 2020, 02:10
3
The correct answer is D) 540 − (c + d+ e)
From the 3 quadrilaterals created within the triangle, we get
a+d + 90 + 90 = 360
=> a + d = 180
=> a = 180 -d ------------> (1)
b+e + 90 + 90 = 360
=> b + e = 180
=> b = 180 -e ------------> (2)
c+f + 90 + 90 = 360
=> c + f = 180
=> f = 180 -c ------------> (3)
Therefore, (1) + (2) + (3) => a + b + f = 180 - d + 18- - e + 180 - c
=> a + b + f = 3(180) - (c+d+e)
= 540 − (c + d+ e)
From the 3 quadrilaterals created within the triangle, we get
a+d + 90 + 90 = 360
=> a + d = 180
=> a = 180 -d ------------> (1)
b+e + 90 + 90 = 360
=> b + e = 180
=> b = 180 -e ------------> (2)
c+f + 90 + 90 = 360
=> c + f = 180
=> f = 180 -c ------------> (3)
Therefore, (1) + (2) + (3) => a + b + f = 180 - d + 18- - e + 180 - c
=> a + b + f = 3(180) - (c+d+e)
= 540 − (c + d+ e)
