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Math Expert V
Joined: 02 Sep 2009
Posts: 58316
In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (01:26) correct 26% (01:35) wrong based on 98 sessions

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Tough and Tricky questions: Geometry.

Attachment: 2014-12-04_1849.png [ 6.56 KiB | Viewed 2058 times ]
In the figure above, m + n = 110. What is the value of o + p ?

A) 70
B) 110
C) 250
D) 270
E) 330

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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As m and n add upto 110 degrees, the third angle in the triangle must be 70 degrees.

We can see the the angle just above this is a vertical angle, so it must also be 70 degrees. So now we know the two angles next to angles O and P (let's call them O' and P') add upto 110 degrees. Also note that all angles making up a straight line must add upto 180 degrees. So, O + O' and P + P' must each add upto 180 degrees--all four add upto 360 degrees. Know this and know that O' + P' add upto 110 yields O + P = 250 degrees.

Choice C
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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1
1
let r be the point of intersection of two lines.
since, m+n= 110
therefore r= 180-110
r=70
Therefore degree of opposite angle= 70
In triangle ORP,
angle POR = 180-o
angle OPR = 180-p
angle ORP = 70

180-o+180-p+70=180
-o-p=-250
o+p=250

Ans = C

PS :- I have used O and P as vertices of triangle just for the sake of explanation.
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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1
In the figure below, a=b
a=180-(m+n) = 180-110 = 70
therefore b= 70
O = b+ 180-P

O+P= b+180 = 70+180 = 250

Attachments 4Dec.png [ 14.39 KiB | Viewed 1925 times ]

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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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2
Answer = C) 250

As vertically opposite angles are same,$$\angle{ACB} = 70^{\circ}$$

Attachment: 2014-12-04_1849.png [ 7.64 KiB | Viewed 1936 times ]

Sum of remaining angles would also be the same

180-o + 180-p = 110

o+p = 360-110 = 250
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Geometry.

Attachment:
2014-12-04_1849.png
In the figure above, m + n = 110. What is the value of o + p ?

A) 70
B) 110
C) 250
D) 270
E) 330

Kudos for a correct solution.

Source: Chili Hot GMAT

The correct answer is C.
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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Well, since the opposites of O and P add up to 110, and these four angles together must measure up to 180+180=360, you just substract 110 from 360 to get 250.

Ans c
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Re: In the figure above, m + n = 110. What is the value of o + p ?  [#permalink]

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_________________ Re: In the figure above, m + n = 110. What is the value of o + p ?   [#permalink] 03 Mar 2019, 04:03
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