Answer:
[tex]k=10[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
so
In this problem
[tex](4k+5)\°+(6k+10)\°=115\°[/tex]
Solve for k
Combine like terms
[tex](10k+15)=115[/tex]
subtract 15 both sides
[tex](10k+15)-15=115-15[/tex]
[tex]10k=100[/tex]
[tex]k=10[/tex]
