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When they ask me the angle between two lines, is it the angle in blue or in red ?

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    Depending on context, it may be either. – 2017-02-10
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    Read comment below written answer: most probably it'd be the blue one, i.e.: the acute one. But as Ivan mentions, this could depend on what you've been given as definition or as what you want to achieve. – 2017-02-10

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It's the angle between the two direction vector of the lines (I'm not sure of the name "direction vector", but if the equation is $y=ax+b$, the direction vector is $(1,a)$).

In your case, the red angle is the correct one.

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    I beg to difer: the direction vectors could perfectly well be "anchored" at the intersection point and then point upwards. In fact, in most uses in geometry, the angle between two lines is *defined* to be the **acute** one (in case there is such, otherwise the lines are perpendicular to each other), and in this case it'd be *the blue* angle. – 2017-02-10
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    @DonAntonio: I've never see that the angle of two line is the acute one. This is the definition I know, but may be it may depend of the context... – 2017-02-10
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    You can read it here: http://planetmath.org/anglebetweentwolines , or here: http://www.math-only-math.com/angle-between-two-straight-lines.html , (note (ii)) , or here: http://www.tpub.com/math2/5.htm ... In **any source I know** it is defined that way, but that's not important now: why do **you** define the direction vector of $\;y=ax+b\;$ as $\;(1,a)\;$ ? Why not $\;(-1,-a)\;$ , say? Or even the same as you but *normalized*, namely $\;\frac1{\sqrt{a^2+1}}(1,a)\;$ ...? – 2017-02-10