Find the acute angle between the lines. Round your answer to the nearest degree.

9 x − y = 3,      8 x + y = 8
y=9x-3,             y=-8x+8

m1 = 9                 m2=-8

 

$${\mathtt{180}}{\mathtt{\,-\,}}{\left|\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{9}}\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(-{\mathtt{8}}\right)}\right|} = {\mathtt{13.465\: \!208\: \!094\: \!812}}$$

 

like CPhill said  about  13 degrees

9 x − y = 3,      8 x + y = 8

 

Let's find the slope of each line

y = 9x - 3         y = -8 + 8

 

And the slope of the first line is 9

And the slope of the second line is -8

 

And taking the tangent inverse of the second line, we have

 

tan-1(-8)  = -82.87°   We need to add 180° to this to get the correct angle = 97.13°

 

And taking the tangent inverse of the first line, we have

 

tan-1(9) = 83.66°

 

So.....subtrating the second result from the first, we have 13.47° = about 13°