Answer:
25°
Step-by-step explanation:
In isosceles triangle KNM, NL is a perpendicular bisector of angle KNM.
This means
[tex]m\angle KNL=m\angle LNM[/tex]
Since
[tex]m\angle KNL=(5x+10)^{\circ}\\ \\m\angle LNM=(6x-1)^{\circ},[/tex]
you have
[tex]5x+10=6x-1\\ \\5x-6x=-1-10\\ \\-x=-11\\ \\x=11[/tex]
No, find the measure of angles KNL and LNM:
[tex]m\angle KNL=(5\cdot 11+10)^{\circ}=65^{\circ}\\ \\m\angle LNM=(6\cdot 11-1)^{\circ}=65^{\circ}[/tex]
and the measure of angle KNM is
[tex]m\angle KNM=m\angle KNL+m\angle LNM=65^{\circ}+65^{\circ}=130^{\circ}[/tex]
Angles adjacent to the base of isosceles triangle are congruent. The sum of the measures of all interior angles is 180°, then
[tex]m\angle K=\dfrac{1}{2}(180^{\circ}-130^{\circ})=25^{\circ}[/tex]
