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

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Math Expert
Joined: 02 Sep 2009
Posts: 54440
In the figure above, if MO = OP, then y =  [#permalink]

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08 Aug 2017, 10:22
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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

Attachment:

2017-08-08_2112_001.png [ 7.25 KiB | Viewed 555 times ]

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Joined: 03 May 2017
Posts: 91
Re: In the figure above, if MO = OP, then y =  [#permalink]

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08 Aug 2017, 10:28
Bunuel wrote:

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

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

Attachment:
2017-08-08_2112_001.png

P= x+y=45; y= 45- x, Hence A.
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Location: India
Concentration: Technology, Strategy
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Re: In the figure above, if MO = OP, then y =  [#permalink]

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08 Aug 2017, 10:53
Bunuel wrote:

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

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

Attachment:
2017-08-08_2112_001.png

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

$$\angle$$ $$OPM = \angle$$ $$OMP = 45^{\circ}$$

$$\angle$$ $$OPM = x^{\circ} + y^{\circ}$$

$$x^{\circ} + y^{\circ} = 45^{\circ}$$

$$y = 45 - x$$

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Joined: 22 May 2016
Posts: 2647
In the figure above, if MO = OP, then y =  [#permalink]

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08 Aug 2017, 12:15
Bunuel wrote:

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

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

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

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In the figure above, if MO = OP, then y =   [#permalink] 08 Aug 2017, 12:15
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