In the figure above, if x = 80 and y = 30, what is the value of k?

Hey Genxer123,

For now let the angle in the middle of m and y (which looks more like a right angle) be called as "n". So we have a straight line with angles m, n & y.
Would you please explain what you mean by " The relation: y, m and the exterior angle (x + k) lie on a straight line."?
What's unclear to me is since exterior angle(x+k) itself is nothing but (y +n), y shouldn't have been stated explicitly in the expression of straight line.Please provide your inputs if I am missing out something here.

By "there is no relation between m and the exterior angle of the triangle(180-m)", what I mean is the distribution of angles lacks any relation within themselves.
If you read the preceding sentence "To determine the value of m, there should have been some relation between m and y", I am trying to get some relation by m=180-(n+y)
Sure, m+n+y = 180 but there is no way we can relate 'm' in term of 'y' in this equation.
I guess my diction might have got you perplexed.
Thank you.