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In the figure above, if MO = OP, then y =

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Joined: 02 Sep 2009
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Kudos [?]: 135405 [0], given: 12692

In the figure above, if MO = OP, then y = [#permalink]

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New post 08 Aug 2017, 09:22
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In the figure above, if MO = OP, then y =

(A) 45 – x
(B) 90 – x
(C) x
(D) 45 + x
(E) 60 + x


[Reveal] Spoiler:
Attachment:
2017-08-08_2112_001.png
2017-08-08_2112_001.png [ 7.25 KiB | Viewed 326 times ]
[Reveal] Spoiler: OA

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Kudos [?]: 135405 [0], given: 12692

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Re: In the figure above, if MO = OP, then y = [#permalink]

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New post 08 Aug 2017, 09:28
Bunuel wrote:
Image
In the figure above, if MO = OP, then y =

(A) 45 – x
(B) 90 – x
(C) x
(D) 45 + x
(E) 60 + x


[Reveal] Spoiler:
Attachment:
2017-08-08_2112_001.png


P= x+y=45; y= 45- x, Hence A.

Kudos [?]: 19 [0], given: 14

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Location: India
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Re: In the figure above, if MO = OP, then y = [#permalink]

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New post 08 Aug 2017, 09:53
Bunuel wrote:
Image
In the figure above, if MO = OP, then y =

(A) 45 – x
(B) 90 – x
(C) x
(D) 45 + x
(E) 60 + x


[Reveal] Spoiler:
Attachment:
2017-08-08_2112_001.png


Given \(MO = OP\). Therefore \(\triangle\) \(MPO\) is isosceles (\(45:45:90\)) triangle.

\(\angle\) \(OPM = \angle\) \(OMP = 45^{\circ}\)

\(\angle\) \(OPM = x^{\circ} + y^{\circ}\)

\(x^{\circ} + y^{\circ} = 45^{\circ}\)

\(y = 45 - x\)

Answer (A)...

Kudos [?]: 334 [0], given: 261

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Joined: 22 May 2016
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Kudos [?]: 398 [0], given: 640

In the figure above, if MO = OP, then y = [#permalink]

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New post 08 Aug 2017, 11:15
Bunuel wrote:
Image
In the figure above, if MO = OP, then y =

(A) 45 – x
(B) 90 – x
(C) x
(D) 45 + x
(E) 60 + x


[Reveal] Spoiler:
Attachment:
2017-08-08_2112_001.png

Right angle at O and leg MO = leg OP: figure is a right isosceles triangle with angle measures 45-45-90.

x + y = 45
y = 45 - x

Answer A

Kudos [?]: 398 [0], given: 640

In the figure above, if MO = OP, then y =   [#permalink] 08 Aug 2017, 11:15
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