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Let 'm' be the third angle of the triangle. The value of k would depend on value of m. k = 180-(x + m) To determine the value of m, there should have been some relation between m and y. Also, there is no relation between m and the exterior angle of the triangle(180-m). So, K can possibly take all the values given in options without violating any rule of triangle.

Waiting for OA to know if there is something that I am missing out here. Thanks for the question.
_________________

------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq

Let 'm' be the third angle of the triangle. The value of k would depend on value of m. k = 180-(x + m) To determine the value of m, there should have been some relation between m and y. Also, there is no relation between m and the exterior angle of the triangle(180-m). So, K can possibly take all the values given in options without violating any rule of triangle.

Waiting for OA to know if there is something that I am missing out here. Thanks for the question.

TaN1213 , I am close to agreeing with your conclusion, that the answer is E.

I don't understand one part of your explanation. You wrote

Also, there is no relation between m and the exterior angle of the triangle(180-m)

I'm a little lost because, perhaps mistakenly, I think there is a relationship between m and the exterior angle = x + k. The relation: y, m and the exterior angle (x + k) lie on a straight line.

(I keep thinking, inaccurately so far, that we can set up two equations, one having to do with the sum of angles on a straight line, and another having to do either with the sum of angles in a triangle, or the sum of two interior angles equaling an exterior angle).

So I'm curious to know what you mean by "no relation" in the quote above? Thanks!

Let 'm' be the third angle of the triangle. The value of k would depend on value of m. k = 180-(x + m) To determine the value of m, there should have been some relation between m and y. Also, there is no relation between m and the exterior angle of the triangle(180-m). So, K can possibly take all the values given in options without violating any rule of triangle.

Waiting for OA to know if there is something that I am missing out here. Thanks for the question.

TaN1213 , I am close to agreeing with your conclusion, that the answer is E.

I don't understand one part of your explanation. You wrote

Also, there is no relation between m and the exterior angle of the triangle(180-m)

I'm a little lost because, perhaps mistakenly, I think there is a relationship between m and the exterior angle = x + k. The relation: y, m and the exterior angle (x + k) lie on a straight line.

(I keep thinking, inaccurately so far, that we can set up two equations, one having to do with the sum of angles on a straight line, and another having to do either with the sum of angles in a triangle, or the sum of two interior angles equaling an exterior angle).

So I'm curious to know what you mean by "no relation" in the quote above? Thanks!

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.
_________________

------------------------------ "Trust the timing of your life" Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq