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tough geometry problem

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by aditi_bc » Tue Oct 21, 2008 10:37 pm
ANS is C. What is OA?
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by jsl » Wed Oct 22, 2008 2:07 am
I'm guessing C too. Definitely not A or B because the opposing angle can move. I'm not the best guy to explain geometry problems because I just "see" the solution in my head and I play with the shape (in my head).

If both of the lines are locked (because the 2 triangles are isoceles), then sliding the lines up and down does not alter the angle of x. Havign said that, I'm not precisely sure what x would be but I'm fairly sure that it's a constant solution and therefore C is the answer.
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by stop@800 » Wed Oct 22, 2008 10:44 pm
Ans is C

A and B alone are insufficient bcoz one side of angle is not fixed.

and the angle will be equal to 45 degree
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by amitabhprasad » Thu Oct 23, 2008 9:43 am
Is the angle 45 ?
I am getting the angle as 67.5 though I am getting answer as "C" as well

My mistake, I see what I missed.
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by rohangupta83 » Thu Oct 23, 2008 5:07 pm
imo C

X = 45 degrees

what's OA?
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by jsl » Fri Oct 24, 2008 12:40 am
rohangupta83 wrote:imo C

X = 45 degrees

what's OA?
How did you actually calculate that X=45? Can you step through the things you inferred?
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by rohangupta83 » Fri Oct 24, 2008 1:34 am
Sure jsl

here it is:

angle P = 90 degress
and

LP + LR + LT = 180...................................1

LRQS + LRSQ + LR = 180..........................2

LRQS = LRSQ (triangle RQS is an isosceles triangle).............3

equating 1 and 2

LP + LR + LT = LRQS + LRSQ + LR

or

90 + LT = LRQS + LRSQ

plugging equation 3 in the above equation

90 + LT = 2LRSQ
LT = 2LRSQ - 90.................eq 4

Now moving on to triangle TSU

LT + LTSU + LTUS = 180............5
LTSU = LTUS (triangle TSU is an isosceles triangle)
LT + 2 LTSU = 180

substituting for LT from equation 4 in equation 5

2LRSQ - 90 + 2LTSU = 180

2LRSQ + 2LTSU = 270

LRSQ + LTSU = 135.............................equation 6

now,

LRSQ + X + LTSU = 180 (angles on a straight line)

plugging equation 6 in the above equation

X + 135 = 180
or X = 45
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