The angle between two lines

[monkeywantsabanana]

Can anyone help me find the angle between the two intersection lines.

x+y= 8
-4y+x= 2

i drew the lines on the plane

(8,0) (0,8)

and

(2,0) (0, -1/2)

i don't know how to find the angle between the two lines.

[TrueTears]

Extend those lines until they intersect the x axis, then find the angles they make with positive x axis, then from your diagram, some simple geometry yields the answer.

[Chavi]

1) Find the gradients of the two lines:

m1=-1
m2=1/4

2) Take ArcTan of both gradients:
m1 = -45 degress
m2= 14.03 degrees

3) m1 - m2 = 59.03 degrees

[stonecold]

Extend those lines until they intersect the x axis, then find the angles they make with positive x axis, then from your diagram, some simple geometry yields the answer.

Yeah, this is the best way.  No one ever taught me, but one day I just realised you could work it all out with geometry. 

[stonecold]

1) Find the gradients of the two lines:

m1=-1
m2=1/4

2) Take ArcTan of both gradients:
m1 = -45 degress
m2= 14.03 degrees

3) m1 - m2 = 59.03 degrees

How do you know which angle?

I found the other one, which was 121 degrees.

[TrueTears]

1) Find the gradients of the two lines:

m1=-1
m2=1/4

2) Take ArcTan of both gradients:
m1 = -45 degress
m2= 14.03 degrees

3) m1 - m2 = 59.03 degrees

How do you know which angle?

I found the other one, which was 121 degrees.

Which is why I discourage people to simply tackle these problems with "step methods". Don't think that each question has a similar approach, the majority of these finding angle problems has a very similar approach but in general you won't know which angle unless you sketch the diagram or do a bit more algebra. There is much more to these rather than just simply equating gradients with tan and finding arctan.

[stonecold]

1) Find the gradients of the two lines:

m1=-1
m2=1/4

2) Take ArcTan of both gradients:
m1 = -45 degress
m2= 14.03 degrees

3) m1 - m2 = 59.03 degrees

How do you know which angle?

I found the other one, which was 121 degrees.

Which is why I discourage people to simply tackle these problems with "step methods". Don't think that each question has a similar approach, the majority of these finding angle problems has a very similar approach but in general you won't know which angle unless you sketch the diagram or do a bit more algebra. There is much more to these rather than just simply equating gradients with tan and finding arctan.

Don't they have to state the acute angle or obtuse angle of intersection, or have I just misinterpreted?

[TrueTears]

Well normally the question will say find the acute or obtuse angle, although you can simply follow the steps to these questions and then at the end if the Q asks for an acute angle and your angle is bigger than 90, so you use 180-your angle, you might get the answer but you won't know what you're doing

[stonecold]

Well normally the question will say find the acute or obtuse angle, although you can simply follow the steps to these questions and then at the end if the Q asks for an acute angle and your angle is bigger than 90, so you use 180-your angle, you might get the answer but you won't know what you're doing

Yeah, that's what I mean.

As this question didn't state obtuse or acute (as far as I can see), aren't there two acceptable answers?

[TrueTears]

Yeah probs who cares lol

[stonecold]

Yeah probs who cares lol

I don't even know why I care haha.  Methods is over. 

Something I never really got my head around although I now see how simple it all is.