Question 329030
The angle that the line makes with respect to the y axis has a relationship to the line. 
The tangent of the angle is equal to the change in y divided by the change in x using trigonmetry. 
But the change in y over the change in x is also the slope of the line. 
{{{m=tan(theta)}}}
Convert both lines to slope intercept form and find their slopes. 
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{{{6x + 2y = 9}}}
{{{2y=-6x+9}}}
{{{y=-3x+9/2}}}
{{{m1=tan(alpha)=-3}}}
{{{alpha=1.893}}}radians
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{{{-5x + 6y = 4}}}
{{{6y=5x+4}}}
{{{y=(5/6)x+2/3}}}
{{{m2=tan(beta)=5/6}}}
{{{beta=0.695}}}radians
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The angle between them {{{X}}} is then 
{{{X=1.893-0.695=1.199}}}radians
{{{X=1.199(360/2pi)=68.629}}}degrees
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{{{drawing(300,300,-10,10,-10,10,grid(1),locate(1,3,X),
graph(300,300,-10,10,-10,10,-3x+9/2,(5/6)x+2/3))}}}