Finding the angle between two lines

[Rocko]

Here is a file i created of a problem I was asked if see if you have what it takes:

 

[vsage]

I hope you don't find this too little help but first fill in all the angles you know. After that, law of sines is your friend.

 

[Rocko]

I believe that to be so, i just haven't been able to find the angle 3 or angle 2, but maybe i am overlooking something.i will study it some more.

 

[Spectre5]

You can find 2 equations that involve angles 2 and 3, then you have two equations and two unknowns

 

[Rocko]

Oh Really, i don't see it! Every equation i come up with has an extra variable.

i have found:
angle 3 + angle 2 = 60degrees
DA sin(95deg)=1000sin(angle2)
or DP sin(120)=1000sin(angle2)
and DP sin (60deg)=DA sin((95deg)

and similar for angle3

 

[Spectre5]

OK...do this:

Extend out the sides AB and DC until they meet. Then you have another triange there...you can find what that angle is using a couple of equations, then you can use it to find angles 2 and 3

 

[Spectre5]

By "that angle", I am referring to the new angle formed by AB and CD :)