Question

Determine the acute angle between the lines 3x - 7y = 21 and 5x + 3y = 15.

Answer 1

angle between two lines if we know the slopes, m1 and m2

tanØ = |(m1 - m2)/(1 + m1m2)|
where Ø is the acute angle

slope of first line = 3/7
slope of 2nd line = -5/3

tanØ = (3/7 + 5/3)/(1 - 5/7)
= (44/21) / (-2/7)
= -22/3

Ø = 180 - 82.23° = 97.77°

or, without the above formula

m1 = 3/7
so the first line makes an angle of 23.199° with the x-axis
m2 = -5/3
so the 2nd line makes an angle of 120.964° with the x-axis
so the angle between them
= 120.964 - 23.199
= 97.77°

Answer 2

However, they wanted the acute angle. So, Sylvia, now it's up to you...