`x + 2y = 8, x - 2y = 2` Find the angle theta (in radians and degrees) between the lines

Given `x+2y=8, x-2y=2`

Find the slope of line 1.

`x+2y=8`

`2y=-x+8`

`y=-1/2x+4`

The slope of line 1 is `m_1=-1/2`

Find the slope of line 2.

`x-2y=2`

`-2y=-x+2`

`y=1/2x-1`

The slope of line 2 is `m_2=1/2.`

Find the angle between the two lines using the formula

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

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

`|` `tan(theta)=|1/(1-1/4)|=1/(3/4)=4/3`

`theta=arctan(4/3)=53.1^@=.9273` radians

The angle between the two lines is 53.1 degrees or .9273 radians.