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In the figure above, what is the value of z ?

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In the figure above, what is the value of z ?  [#permalink]

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New post 10 Feb 2019, 05:08
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

77% (02:35) correct 23% (03:40) wrong based on 26 sessions

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In the figure above, what is the value of z ?

A. 40
B. 45
C. 50
D. 55
E. 65

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In the figure above, what is the value of z ?  [#permalink]

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New post Updated on: 13 Feb 2019, 22:26
1

Solution



To find:
• The value of z, as per the figure

Approach and Working:
Image

As per the figure,
    • Angle ABE + angle CBE = 180
    Or, angle CBE = 180 – 85 = 95
    • Angle AEB + angle DEB = 180
    Or, angle DEB = 180 – (x + 15) = 165 – x

Now, in the quadrilateral BCDE,
    • EBC + BCD + CDE + DEB = 360
    Or, 95 + 2x – 5 + 65 + 165 – x = 360
    Or, 320 + x = 360
    Or, x = 40

Also, in triangle ABE,
    • ABE + BEA + EAB = 180
    Or, 85 + x + 15 + z = 180
    Or, 85 + 40 + 15 + z = 180
    Or, 140 + z = 180
    Or, z = 40

Hence, the correct answer is option A.

Answer: A

Image

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Originally posted by EgmatQuantExpert on 10 Feb 2019, 05:22.
Last edited by EgmatQuantExpert on 13 Feb 2019, 22:26, edited 1 time in total.
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Re: In the figure above, what is the value of z ?  [#permalink]

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New post 10 Feb 2019, 05:31
SajjadAhmad wrote:
Attachment:
00000.jpg


In the figure above, what is the value of z ?

A. 40
B. 45
C. 50
D. 55
E. 65



we can solve by first detetmining value of x
for quadrilateral =
95+2x-5+65+165-x=360
x= 40

now for triangle
85+55+z=180
z=40
IMOA
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Re: In the figure above, what is the value of z ?   [#permalink] 10 Feb 2019, 05:31
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