`5x + 2y = 16, 3x - 5y =- 1` Find the angle theta (in radians and degrees) between the lines

Given

`5x+2y=16`  

`3x-5y=-1`

Find the slope of line 1.

`5x+2y=16`

`2y=-5x+16`

`y=-5/2x+8`

The slope of line 1 is `m_1=-5/2.`

Find the slope of line 2.

`3x-5y=-1`

`-5y=-3x-1`

`y=3/5x+1/5`

The slope of line t is `m_2=3/5.`

Find the angle between the lines using the formula

`tan(theta)=|(m_2-m_1)/(1+m_1m_2)|`

`tan(theta)=|((3/5)-(-5/2))/(1+(-5/2)(3/5))|=31/5`

`theta=tan^-1 (31/5)=80.8^@=1.4109`  radians.

The angle between the lines is 80.8 degrees or 1.4109 radians.