pratu043
In the given figure, AB divides DAC in the ratio 1:3 and AB = DB. Calculate the unknown angles.
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pratu043
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dw:1342757653054:dw
pratu043
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@lgbasallote please help!!
lgbasallote
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dw:1342757791245:dw
just presenting a drawing first so i can visualize it
pratu043
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I figured out that angle ADB = y.
lgbasallote
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how did you figure that out?
lgbasallote
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oh i see
pratu043
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Because triangle ABD is isosceles.
lgbasallote
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dw:1342757924763:dw
pratu043
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And how did you get DB = 3a and BC = a?
lgbasallote
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it says the ratio is 1:3
pratu043
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Ratio is 1:3 for the angle DAC.
pratu043
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That means t = 3a and y = a.
lgbasallote
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oh lol
lgbasallote
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y + y + t + 90 = 180
2y + t = 90
do you see this?
pratu043
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How did you get x = 90 degrees? I know it looks like that but i doesn't say so in the question.
pratu043
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Yes, I got that.
lgbasallote
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according to your triangle it's a right triangle
pratu043
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I might be slightly greater or lesser that 90 right?
lgbasallote
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dw:1342758203033:dw
y + y + m = 180
t + 90 + n = 180
m + n = 180
pratu043
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*It.
lgbasallote
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what do you mean?
lgbasallote
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do you have the *real* drawing??
lgbasallote
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this drawing is getting confusing :(
pratu043
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Yes, but it is in the form of a worksheet that I got in school(it is not in the electronic form).
pratu043
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I'll try drawing again then, just a minute.
pratu043
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dw:1342758349890:dw
pratu043
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dw:1342758495805:dw
For convenience.
pratu043
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The question given along with the drawing is the original one at the top and as you can see, there's nothing saying x is a right angle.
lgbasallote
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dw:1342758686754:dw
a + a + x = 180
n + 3a + x = 180
a + a + m = 180
m + n = 180
do you see these?
pratu043
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Yes I do.
lgbasallote
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so you have 4 unknowns and 4 equations. we can use systems of linear equations
pratu043
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Yeah, but I only know how to solve system of equations with 2 variables.
lgbasallote
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i wrote one wrong...should be a + (a+3a) + x = 180
pratu043
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So 5a + x = 180
lgbasallote
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a + a + 3a + x = 180 >1
n + 3a + x = 180 > 2
a + a + m = 180 >3
m + n = 180 > 4
yes
lgbasallote
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let's simplify everything first
5a +x = 180
n + 3a + x = 180
2a + m = 180
m + n = 180
pratu043
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OK. What next?
lgbasallote
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now we subtract equation 2 from equation 1
5a + x = 180

3a + x + n = 180
===========
2a + 0 + n = 0
===========
2a + n = 0
===========
2a = n
lgbasallote
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^that would be equation 5
pratu043
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Shouldn't it be 2a = n?
Because 0  n would be n and but you wrote n.
lgbasallote
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uhmm yeah you're right 2a = n
pratu043
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So a = n/2.
Or we can use n = 2a in one of the equations?
lgbasallote
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2a = n is the 5th equation
pratu043
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5a +x = 180
n + 3a + x = 180
2a + m = 180
m + n = 180
2a = n
lgbasallote
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now look at m + n = 180
i can also say n = 180  m <i'll substitute this into the 2nd equation
n + 3a + x = 180
180 m + 3a + x = 180
3a  m + x = 0 <6th equation
pratu043
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Are you sure this is 9th standard level? Because our math teacher hasn't taught us this yet. We have only reached linear equations in two variables.
lgbasallote
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well...x is not 90 degrees....
lgbasallote
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it's seriously complicated
pratu043
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dw:1342759662640:dw
lgbasallote
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if x were 90 then i assume the right triangle postulates and theorems could be applied
lgbasallote
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or maybe im just doing something wrong here...
lgbasallote
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@dpaInc
pratu043
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Angle ABC = 180  (3a + x).
pratu043
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a + 4a + x = 180
or 5a + x = 180
pratu043
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This is still not getting us anywhere ....
pratu043
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dw:1342759792383:dw
pratu043
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Is it possible to get x in terms of a ?
lgbasallote
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@dpaInc help here
pratu043
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dw:1342760301927:dw
If we take XY parallel to AB then AC is a transversal.
pratu043
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@dpaInc you should find a, 3a and x.(in the latest figure)
pratu043
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Are you there @dpaInc?
dpaInc
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yep... just trying to figure it out....:)
dpaInc
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dw:1342761130552:dw
dpaInc
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i don't think the there is a unique solution....
are you looking for integer solutions?
pratu043
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I have to go now. Please please please help if possible .....
mukushla
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i think dplanc is right
there is no unique solution unless x=90