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In the given figure, AB divides DAC in the ratio 1:3 and AB = DB. Calculate the unknown angles.

Mathematics
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|dw:1342757653054:dw|
@lgbasallote please help!!
|dw:1342757791245:dw| just presenting a drawing first so i can visualize it

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Other answers:

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

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