In the figure shown, what is the value of x?

Mom4MBA wrote:after checking that each statement alone will not do any good we will check both the statements together. so use the basic properties or triangles and quadrilaterals and start working.



take the big triangle:

sum of the three angles = 180
180-2a + 180-2b + 90 = 180
a+b = 135

now take the quadrilateral:

sum of the 4 angles = 360
180-a + 180-b + x + 90 = 360
x= a+b - 90
x= 135 - 90
x= 45[/img][/url]

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Thanks,that was really appreciative.Normally,geometry problems take too much time.It is always handy to know the shortcuts.Nevertheless,GMATQuantCoach's method was quite comprehensive,but I think a bit time-taking but also brain-racking.For preparation,I think it is ok but in the GMATprep and on the actual GMAT,I would also like to know the shortcuts.GMATQuantCoach-Do you also have any shortcut methods for solving such geometry problems??

yea even i would like to know !
i am quite awrite in geometry ;-(

harsh.champ wrote:

Mom4MBA wrote:after checking that each statement alone will not do any good we will check both the statements together. so use the basic properties or triangles and quadrilaterals and start working.



take the big triangle:

sum of the three angles = 180
180-2a + 180-2b + 90 = 180
a+b = 135

now take the quadrilateral:

sum of the 4 angles = 360
180-a + 180-b + x + 90 = 360
x= a+b - 90
x= 135 - 90
x= 45[/img][/url]

_____________
Thanks,that was really appreciative.Normally,geometry problems take too much time.It is always handy to know the shortcuts.Nevertheless,GMATQuantCoach's method was quite comprehensive,but I think a bit time-taking but also brain-racking.For preparation,I think it is ok but in the GMATprep and on the actual GMAT,I would also like to know the shortcuts.GMATQuantCoach-Do you also have any shortcut methods for solving such geometry problems??

Mom4MBA wrote:after checking that each statement alone will not do any good we will check both the statements together. so use the basic properties or triangles and quadrilaterals and start working.



take the big triangle:

sum of the three angles = 180
180-2a + 180-2b + 90 = 180
a+b = 135

now take the quadrilateral:

sum of the 4 angles = 360
180-a + 180-b + x + 90 = 360
x= a+b - 90
x= 135 - 90
x= 45[/img][/url]

mom4MBA if you are still active here, your method was really understandable, Thank you

Only I just saw another branch of your method

a+b= 135 and from Diagram a+b+x= 180 ( as AXB is a straight angle = 180)
so x= 180-135= 45

( no need to consider the quadrilateral, again couldn't have seen this without your initial steps, thank you )