# Determine angle measure from two slopes?

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Is it possible to find the angle measure of two lines following y=mx+b format? I didn't think so because it is impossible to determine the slope of a vertical line, but I also could be wrong. I tried to relate two slopes to their definite angle measures. I used slopes 1 and -1 for 90 degrees, and 1 and 0 for 45 degrees. I can't find any relationship after using multiple slopes, so I don't know if there is already a way.

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I'm confused about what you're actually asking. Perhaps a diagram would be of assistance?

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Perhaps you could use the $y = mx +b$ to find a vector for each line and then use the scalar product?

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The acute angle θ between two straight lines is given by:

$\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|$

Where m1 and m2 are the gradients of the lines.

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Let's make a right-angled triangle with $y=mx+c$ as it's hypotenuse. If it's horizontal base is 2 units long, then it's hieght will be 2m.

Now on to some easy trig:

$\tan\theta=\frac{opp}{adj}$

Factor in the sides of our triangle.

$\tan\theta=\frac{2m}{2}$

Re-arange.

$\theta=\tan^{-1}\frac{2m}{2}$

If I got that right (no garuntees) then the 2 can be replaced with whatever makes life easy.

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