Respuesta :
An angle is formed when two lines intersect.
The lines forming the angle ABC are lines AB and BC
We need to find the angle between these lines before we can get the measure of angle B.
Firstly we need to write out the coordinates of each of the points.
The coordinates of point A is (-6,-1)
The coordinates of point B is (-1,-2)
The coordinates of point C is (-3,-3)
Now, to be able to find the angle between the lines, we need to get the equation of the two lines
We start with the line AB
The points involved are (-6,-1) and (-1,-2)
The slope of this line is calculated as;
m = (y2-Y1)/(x2-x1)
m = (-2+1)/(-1 + 6) = -1/5
The equation of the line can thus be written as
y = -1/5x + c
To get c, we simply substitute the coordinates of one of the points;
-2 = -1/5(-1) + c
-2 = 1/5 + c
c = -2 -1/5 = -11/5
So the equation of line AB is
y = -1/5x - 11/5
However, kindly note that to find the angle between two lines, knowing the slope of both lines alone woukd suffice.
Let us now calculate the slope of line BC
The points involved are
(-1,-2) and (-3,-3)
So the slope m is;
m = (y2-y1)/(x2-x1) = (-3 + 2)/(-3+ 1) = -1/-2 = 1/2
So we want to find the angle between two lines with slope -1/5 and 1/2
The angle between two lines given the slope can be measured using the equation;
tan θ = (m2-m1) / (1+m1m2)
In this case m1 = -1/5 and m2 = 1/2
So substitute these values in the equation above;
tan θ = (1/2 + 1/5)/(1 - 1/10)
tan θ = (0.5 + 0.2)/(0.9)
tan θ = 0.7/0.9
tan θ= 0.778
θ = arc tan 0.778
θ = 37.875 which is 38 degrees to the nearest degree
We repeat same process to get the value of angle ACB
The lines involved here are lines AC and BC
Then we add the angle here to that of ABC
and finally, to get the angle CAB, we subtract the addition of this angle from 180
Recall the total measure of angles in a triangle is 180
And thus;
ABC + ACB + CAB = 180
SO CAB = 180 - ABC - ABC
