Question

Help with finding the angle between two lines true or false question

Answer 1

The angle between two lines will always be given by the acute angle that is formed when the two lines intersect.

Answer 2

I believe this is false:
Two lines in the plane will either be parallel or intersecting. If they intersect, then the place where the two lines intersect forms two pairs of supplementary angles. One pair will be acute, the other obtuse

@freckles is this good evidence for it to be false?

Answer 3

if the two lines intersect then the angle will be given by \[\theta=\arctan(|\frac{m_1-m_2}{1+m_1 m_2}|)\]
so theta will me a number between 0 and 90 degree

Answer 4

which is either acute or right angle

Answer 5

well that is true


and your true/or false question is weird
I assume they wanted to use that formula I was talking about
but angles between two lines can also be obtuse (and you find the obtuse angle by doing 180-the above theta I wrote)

Answer 6

They gave me another formula for the lesson:

Subtract the angles of inclination of the two lines from one another (the larger angle of inclination minus the smaller angle of inclination). If the result of doing so is greater than 90°, find the correct angle between the two lines by subtracting this result from 18

Answer 7

I didnt just learn that one :p

Answer 8

180*

Answer 9

The angle between two lines will always be given by the acute angle that is formed when the two lines intersect.


why must the angle between two lines always be given by the acute angle where the intersection happens?

why can't it be given by the obtuse angle?

you notice in all your questions it says to find the angle between the two lines and we always found the acute one? we did not one time try to find the obtuse angle? it is like your lesson decided that the angle they wanted was always going to be the acute angle (like it was understood or something)

but as you said the angle can be right
say we have slopes that are opposite reciprocals of one another
\[m_1 \text{ and } \frac{-1}{m_1} \\ |m_1-\frac{-1}{m_1}|=|\frac{m_1^2+1}{m_1}| \\ |1+m_1 \cdot \frac{-1}{m_1}|=|1-1|=|0| \\ \tan(\theta)=\text{ undefined }\]
so in a way you are techically not supose to use that formula we mentioned to find the angle between two lines that are perpendicular

like
\[\theta=\arctan(|\frac{m_1-m_2}{1+m_1m_2}|) \text{ will output a } \theta \in [0,\frac{\pi}{2})\]
so it actually doesn't include the 90 deg

but also you kinda use that formula depending on if you know a little bit about limits
\[n->\infty \\tan(\theta)=n \\ \theta=\arctan(n)=\frac{\pi}{2}\]

Answer 10

like this is what I'm saying:

you lesson never said to find the acute angle between the lines, right?
it said find the angles between the lines?

Answer 11

angle between the lines*

Answer 12

didn't mean to make angle plural

Answer 13

Yes it never did ask for the specific type of angle

Answer 14

and the thing is that formula we are using was always going to give us something between 0 and 90 degs

so I kinda think they are looking for true here

Answer 15

You are correct

Answer 16

I still think it is dumb

Answer 17

They were indeed looking for true. That whole sentence that I mentioned above got me so confused though.

Answer 18

"Two lines in the plane will either be parallel or intersecting. If they intersect, then the place where the two lines intersect forms two pairs of supplementary angles. One pair will be acute, the other obtuse"

Answer 19

thats why I was unsure this whole time and with that formula i also posted

Answer 20

I guess they were assuming that you wouldn't have a 90 angle between the intersecting lines which you could have


and yes supplementary means they add up to 180 deg

the theta we get from
\[\theta=\arctan(|\frac{m_1-m_2}{1+m_1 m_2}|)\]
will be the acute angle between the lines

and \[180-\theta=180-\arctan(|\frac{m_1-m_2}{1+m_1m_2}|)\]
will be the obtuse angle

and yea when you add t+(180-t) you get 180
so the angles are definitely supplementary

Answer 21

Alrights Thank you for your help

Answer 22

np

Answer 23

Can confirm trying to close out my semester 2 weeks early. So trying to complete precal within the next week :p already got 3 classes basically done