Find the Angle $\alpha$ Between Two Nonvertical Lines $L _ { 1 } \text { and } L _ { 2 }$

question 13

Multiple Choice

Find the angle $\alpha$ between two nonvertical lines $L _ { 1 } \text { and } L _ { 2 }$ . The angle $\alpha$ 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 $m _ { 1 } m _ { 2 } \neq - 1$ .)
$\begin{array} { l } L _ { 1 } : 3 x - 2 y = 5 \\L _ { 2 } : x + y = 1\end{array}$
Round your answer to one decimal place.

• A) \(78.7 ^ { \circ }\)
• B) \(79.7 ^ { \circ }\)
• C) \(81.7 ^ { \circ }\)
• D) \(80.7 ^ { \circ }\)
• E) \(82.7 ^ { \circ }\)