Question

Triangle Z Y X is shown with its exterior angles. Line Z X extends through point N. Line X Y extends to point M. Line Y Z extends to point L. Angle Y Z X is (4 k + 5) degrees. Angle Y X Z is (6 k + 10) degrees. Angle M Y Z is 115 degrees.
What is the value of k?

Answer 1

k = 10

Reason: The exterior angle at Y (angle M Y Z) equals the sum of the two remote interior angles:
115 = (4k + 5) + (6k + 10) = 10k + 15 → 10k = 100 → k = 10.