Question

Triangle KNM is isosceles, where angle N is the vertex.

Answer 1

Answer:

It's B. on edge 2020

Step-by-step explanation:

25°

Answer 2

Answer:

25°

Step-by-step explanation:

In isosceles triangle KNM, NL is a perpendicular bisector of angle KNM.

This means

$m\angle KNL=m\angle LNM$

Since

$m\angle KNL=(5x+10)^{\circ}\\ \\m\angle LNM=(6x-1)^{\circ},$

you have

$5x+10=6x-1\\ \\5x-6x=-1-10\\ \\-x=-11\\ \\x=11$

No, find the measure of angles KNL and LNM:

$m\angle KNL=(5\cdot 11+10)^{\circ}=65^{\circ}\\ \\m\angle LNM=(6\cdot 11-1)^{\circ}=65^{\circ}$

and the measure of angle KNM is

$m\angle KNM=m\angle KNL+m\angle LNM=65^{\circ}+65^{\circ}=130^{\circ}$

Angles adjacent to the base of isosceles triangle are congruent. The sum of the measures of all interior angles is 180°, then

$m\angle K=\dfrac{1}{2}(180^{\circ}-130^{\circ})=25^{\circ}$