In the given figure, AB divides DAC in the ratio 1:3 and AB = DB. Calculate the unknown angles.
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 anonymous
In the given figure, AB divides DAC in the ratio 1:3 and AB = DB. Calculate the unknown angles.
 katieb
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 anonymous
dw:1342757653054:dw
 anonymous
@lgbasallote please help!!
 lgbasallote
dw:1342757791245:dw
just presenting a drawing first so i can visualize it
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 anonymous
I figured out that angle ADB = y.
 lgbasallote
how did you figure that out?
 lgbasallote
oh i see
 anonymous
Because triangle ABD is isosceles.
 lgbasallote
dw:1342757924763:dw
 anonymous
And how did you get DB = 3a and BC = a?
 lgbasallote
it says the ratio is 1:3
 anonymous
Ratio is 1:3 for the angle DAC.
 anonymous
That means t = 3a and y = a.
 lgbasallote
oh lol
 lgbasallote
y + y + t + 90 = 180
2y + t = 90
do you see this?
 anonymous
How did you get x = 90 degrees? I know it looks like that but i doesn't say so in the question.
 anonymous
Yes, I got that.
 lgbasallote
according to your triangle it's a right triangle
 anonymous
I might be slightly greater or lesser that 90 right?
 lgbasallote
dw:1342758203033:dw
y + y + m = 180
t + 90 + n = 180
m + n = 180
 anonymous
*It.
 lgbasallote
what do you mean?
 lgbasallote
do you have the *real* drawing??
 lgbasallote
this drawing is getting confusing :(
 anonymous
Yes, but it is in the form of a worksheet that I got in school(it is not in the electronic form).
 anonymous
I'll try drawing again then, just a minute.
 anonymous
dw:1342758349890:dw
 anonymous
dw:1342758495805:dw
For convenience.
 anonymous
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
dw:1342758686754:dw
a + a + x = 180
n + 3a + x = 180
a + a + m = 180
m + n = 180
do you see these?
 anonymous
Yes I do.
 lgbasallote
so you have 4 unknowns and 4 equations. we can use systems of linear equations
 anonymous
Yeah, but I only know how to solve system of equations with 2 variables.
 lgbasallote
i wrote one wrong...should be a + (a+3a) + x = 180
 anonymous
So 5a + x = 180
 lgbasallote
a + a + 3a + x = 180 >1
n + 3a + x = 180 > 2
a + a + m = 180 >3
m + n = 180 > 4
yes
 lgbasallote
let's simplify everything first
5a +x = 180
n + 3a + x = 180
2a + m = 180
m + n = 180
 anonymous
OK. What next?
 lgbasallote
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
^that would be equation 5
 anonymous
Shouldn't it be 2a = n?
Because 0  n would be n and but you wrote n.
 lgbasallote
uhmm yeah you're right 2a = n
 anonymous
So a = n/2.
Or we can use n = 2a in one of the equations?
 lgbasallote
2a = n is the 5th equation
 anonymous
5a +x = 180
n + 3a + x = 180
2a + m = 180
m + n = 180
2a = n
 lgbasallote
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
 anonymous
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
well...x is not 90 degrees....
 lgbasallote
it's seriously complicated
 anonymous
dw:1342759662640:dw
 lgbasallote
if x were 90 then i assume the right triangle postulates and theorems could be applied
 lgbasallote
or maybe im just doing something wrong here...
 lgbasallote
 anonymous
Angle ABC = 180  (3a + x).
 anonymous
a + 4a + x = 180
or 5a + x = 180
 anonymous
This is still not getting us anywhere ....
 anonymous
dw:1342759792383:dw
 anonymous
Is it possible to get x in terms of a ?
 lgbasallote
@dpaInc help here
 anonymous
dw:1342760301927:dw
If we take XY parallel to AB then AC is a transversal.
 anonymous
@dpaInc you should find a, 3a and x.(in the latest figure)
 anonymous
Are you there @dpaInc?
 anonymous
yep... just trying to figure it out....:)
 anonymous
dw:1342761130552:dw
 anonymous
i don't think the there is a unique solution....
are you looking for integer solutions?
 anonymous
I have to go now. Please please please help if possible .....
 anonymous
i think dplanc is right
there is no unique solution unless x=90
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