Precalculus, Chapter 10, 10.1, Section 10.1, Problem 52

Given:
3x-5y=3
3x+5y=12

The formula to find the angle between two lines is
tan(theta)=|(m_2-m_1)/(1+m_1_2)|

Find the slope of line 1.
3x-5y=3
-5y=-3x+3
y=3/5x-3/5
The slope of line 1 is m_1=3/5 .
Find the slope of line 2.
3x+5y=12
5y=-3x+12
y=-3/5x+12/5
The slope of line 2 is m_2=-3/5.
Plug in the slopes into the formula
tan(theta)=|((m_2-m_1)/(1+m_1m_2))|
tan(theta)=|((-3/5)-(3/5))/(1+(3/5)(-3/5))|=15/8

theta=arctan(15/8)=61.9^@=1.0808 radians.

The angle between the two lines is 61.9 degrees or 1.0808 radians.