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# x < 90

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x < 90 [#permalink]  16 May 2018, 08:52
Expert's post
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Question Stats:

80% (01:07) correct 20% (03:18) wrong based on 15 sessions
Attachment:

triangle.jpg [ 12.2 KiB | Viewed 422 times ]

$$x < 90$$

 Quantity A Quantity B y 70
[Reveal] Spoiler: OA

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Manager
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Re: x < 90 [#permalink]  16 May 2018, 09:15
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As sum of 3 angles in triangle is 180 and angle at any straight side is 180 degrees.

If x is les than 90 the other angle in the triangle on other side is greater than 90 and hence the y can have values only les than 70

20+ 90 = 110
But based on value of x, the value of other 2 angles can only be greater than 110 hence B
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Re: x < 90 [#permalink]  16 May 2018, 09:32
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Expert's post
Carcass wrote:
Attachment:
triangle.jpg

$$x < 90$$

 Quantity A Quantity B y 70

If angle x is less than 90 degrees, we can express this as follows...

NOTE: (90-)° does NOT mean "negative 90 degrees"; that notation means "an angle that's less than 90 degrees"

Since angles on a line must add to 180°, we can conclude that the other angle must be more than 90 degrees, which we'll express as follows:

At this point, we know that the 3 angles in the triangle must add to 180°
So, we can write: y + 20 + (90+) = 180
Notice that 20 + (90+) = 110+ (an angle that greater than 110 degrees)
So, we can write: y + (110+) = 180

If the equation were y + 110 = 180, then we'd conclude that y EQUALS 70
However, since the equation is y + (110+) = 180, we can conclude that y is LESS THAN 70

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: x < 90   [#permalink] 16 May 2018, 09:32
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