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

Explanation:

Answer 2

k=10

Explanation:

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

In this problem

m∠YZX+m∠YXZ=m∠MYZ

substitute the given values

`(4k+5)\°+(6k+10)\°=115\°`

Solve for k

`10k+15=115\\10k=100\\k=10`