Find the angle ? between two nonvertical lines $$L _ { 1 }$$ and $L _ { 2 }$ .The angle ? satisfies the equation? $$\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right|$$ ? where $m _ { 1 }$ and $m _ { 2 }$ are slopes of $L _ { 1 }$ and $L _ { 2 }$ ,respectively.
(Assume that $m _ { 1 } m _ { 2 } \neq 1$ . )? $L _ { 1 }$ : 5x - 4y = 5 $L _ { 2 }$ : x + y = 1
?
Round your answer to one decimal place.
?
A)83.7º
B)84.7º
C)85.7º
D)86.7º
E)87.7º

Question

Quizplus · Accepted Answer

The equation of line $L _ { 1 }$ is 5x - 4y = 5, which can be written in slope-intercept form as y = \frac { 5 } { 4 } x - \frac { 5 } { 4 }. Therefore, the slope of $L _ { 1 }$ is $m _ { 1 } = \frac { 5 } { 4 }$.The equation of line $L _ { 2 }$ is x + y = 1, which can be written in slope-intercept form as y = -x + 1. Therefore, the slope of $L _ { 2 }$ is $m _ { 2 } = -1$.Using the formula for the angle between two nonvertical lines, we have:$$\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right| = \left| \frac { -1 - \frac { 5 } { 4 } } { 1 + (-1) \left( \frac { 5 } { 4 } \right) } \right| = \left| \frac { -9 / 4 } { 1 - 5 / 4 } \right| = \left| \frac { -9 / 4 } { -1 / 4 } \right| = 9$$Therefore, $\alpha = \tan ^ { - 1 } ( 9 ) \approx 83.7^\circ$.

Find the Angle ? Between Two Nonvertical Lines L1L _ { 1 }L1​

Find the Angle ? Between Two Nonvertical Lines $L _ { 1 }$