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In the figure above a + b + f =

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In the figure above a + b + f = [#permalink] New post 07 May 2020, 06:13
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84% (01:33) correct 15% (02:43) wrong based on 19 sessions
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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)

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[Reveal] Spoiler: OA

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Re: In the figure above a + b + f = [#permalink] New post 07 May 2020, 06:43
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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)
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Re: In the figure above a + b + f = [#permalink] New post 09 Oct 2020, 02:10
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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)
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Re: In the figure above a + b + f = [#permalink] New post 10 Oct 2020, 06:37
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Let a+b+c =360 they form a circle

d+e+f=180 sum of angles in a triangle.

a+b+f is what we are asked to find

so first a+b=360-c
then f=180-d-e

add these two
we get 360-c+180-d-e
540-c-d-e
So 540 -(c+d+e)

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Re: In the figure above a + b + f =   [#permalink] 10 Oct 2020, 06:37
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