anonymous
  • anonymous
In the given figure, AB divides DAC in the ratio 1:3 and AB = DB. Calculate the unknown angles.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1342757653054:dw|
anonymous
  • anonymous
@lgbasallote please help!!
lgbasallote
  • lgbasallote
|dw:1342757791245:dw| just presenting a drawing first so i can visualize it

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

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