In the diagram, Find the value of w

-13

Step-by-step explanation:

the angle of ACD is 180-72 = 108 degrees.

simply because every side of a line represents 180 degrees of turning potential (to flip something around on a flat ground is a 180 degree turn). and we know 72 degrees are already "taken" at the other side of the angle.

BC bisects the angle. that means it divided the angle into 2 equal parts.

so the angle between BC and k is 108/2 = 54 degrees.

because j is parallel to k, this angle is the same as the angle between BC and j.

so,

54 = 2w + 80

-26 = 2w

w = -13