Answer:
The angle between AB and BC= 41,63°
Explanation:
Two vectors are given.
Sometimes it helps if you change the j for x and the i for y.
AB= 2y + x
2y + x = 0
2y = -x
y = - 1/2x
BC= 2y + 5x
2y + 5x = 0
2y = -5x
y = - 5/2x
Both lines AB and BC intersect in point (0,0)
The angle between AB and BC can be constructed in a graph.
y = - 1/2x
y = - 5/2x
Measureing the angle between the lines gives you an estimate of the angle. I measured 43°. See the attachment.
The angle of a line with the x-axis, is mathematically the same as the incline or gradient of the line, which is the same as the tan of Alpha.
AB has a gradient of - 1/2
So tan(Alpha) = - 1/2
there fore Alpha = arctan( - 1/2 ) = -26,6 °
BC haa a gradient of - 52
So tan(Beta) = - 5/2
there fore Beta = arctan( - 5/2 ) = -86,2°
Angle between AB and BC
-86,2 - -26,6
-86,2 + 26,6
-41,6°
That corner is the same as 41,6°
The angle between AB and BC= 41,6°