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In the figure above, what is the sum of x and y in terms of
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06 May 2020, 15:14
06 May 2020, 15:14
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Question Stats:
75% (02:07) correct
24% (02:57) wrong based on 58 sessions
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#greprepclub In the figure above, what is the sum of x and y in terms of z.jpg [ 23.48 KiB | Viewed 6140 times ]
In the figure above, what is the sum of x and y in terms of z ?
A. \(z + 90\)
B. \(\frac{z}{2}+90\)
C. \(180-2z\)
D. \(180-\frac{z}{2}\)
E. \(z+180\)
Re: In the figure above, what is the sum of x and y in terms of
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06 May 2020, 17:01
06 May 2020, 17:01
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As mentioned in the fig.
From triangle MNP; angle a = 180-(x+y)
from triangle PNQ; angle b = 180-(x+y)
On a straigth line MNO; angle a + angle b + angle z = 180
180-(x+y) + 180-(x+y) + z = 180
z + 180 = 2(x+y)
z/2 + 90 = x+y
From triangle MNP; angle a = 180-(x+y)
from triangle PNQ; angle b = 180-(x+y)
On a straigth line MNO; angle a + angle b + angle z = 180
180-(x+y) + 180-(x+y) + z = 180
z + 180 = 2(x+y)
z/2 + 90 = x+y
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#what is the sum of x and y in terms of z.jpg [ 17.57 KiB | Viewed 5954 times ]
Re: In the figure above, what is the sum of x and y in terms of
[#permalink]
08 May 2020, 07:32
08 May 2020, 07:32
2
Let angle PNQ= a
then we can say a+ z= angle NPM + angle MNP= x+y(ext angle property of triangle)
therefore a+z=x+y...............................(i)
now in triangle PNQ
a= 180-x-y(angle sum property of triangle )......................(ii)
therefore
180-x-y + z = x+y from i and ii
x+y= 90+z/2
B
then we can say a+ z= angle NPM + angle MNP= x+y(ext angle property of triangle)
therefore a+z=x+y...............................(i)
now in triangle PNQ
a= 180-x-y(angle sum property of triangle )......................(ii)
therefore
180-x-y + z = x+y from i and ii
x+y= 90+z/2
B
