Answer:
81.87°
Step-by-step explanation:
The angle a line makes with the x-axis is equal to the arctangent of its slope. Here, L1 makes an angle of arctan(0.5) = 26.57° with the x-axis; L2 makes an angle of arctan(-3) = -71.57° with the x-axis. The difference between these angles is ...
26.57° -(-71.57°) ≈ 98.13° . . . . . . all numbers rounded to 2 decimal places
This is an obtuse angle, so the acute angle is ...
180° -98.13° = 81.87°
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You can also use the trig formula for the difference of angles. Tan(α) is the slope of the first line, 0.5. Tan(β) is the slope of the second line, -3.
tan(α-β) = (tan(α)-tan(β))/(1 +tan(α)tan(β))
tan(angle) = (0.5 -(-3))/(1 +(0.5)(-3)) = 3.5/(-0.5) = -7
angle = arctan(-7) = -81.87°
The angle between the two lines is 81.87°.
