`x - 2y = 7, 6x + 2y = 5` Find the angle theta (in radians and degrees) between the lines

Given: 

`x-2y=7`

`6x+2y=5`

Find the slope for line 1.

`x-2y=7`

`-2y=-x+7`

`y=1/2x-7/2`

The slope of line 1 is `m_1=1/2.`

Find the slope of line 2.

`6x+2y=5`

`2y=-6x+5`

`y=-3x+5/2`

The slope line 2 is `m_2=-3.`

Find the slope between two lines using the formula

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

`tan(theta)=|((-3)-(1/2))/(1+(1/2)(-3))|=7`

`theta=arctan(7)=81.9^@=1.4289` radians

The angle between the two lines is 81.9 degrees or 1.4289 radians.