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In the figure above, what is the sum of x and y in terms of

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In the figure above, what is the sum of x and y in terms of [#permalink] New post   06 May 2020, 15:14
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A
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C
D
E

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In the figure above, what is the sum of x and y in terms of z ?

A. z+90

B. z2+90

C. 180−2z

D. 180−z2

E. z+180
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B
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Re: In the figure above, what is the sum of x and y in terms of [#permalink] New post   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
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Re: In the figure above, what is the sum of x and y in terms of [#permalink] New post   08 May 2020, 07:32
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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
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Re: In the figure above, what is the sum of x and y in terms of [#permalink] New post   01 Aug 2024, 15:43
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Re: In the figure above, what is the sum of x and y in terms of [#permalink]
01 Aug 2024, 15:43
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