Question

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

Isosceles triangle K N M is shown. N L is a perpendicular bisector of angle K N M. Angle K N L is (5 x + 10) degrees and angle L N M is (6 x minus 1) degrees.

What is the measure of angle K?
11º
25º
50º
65º

Answer 1

25 Degrees

Explanation:

Answer 2

25°

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=(1)/(2)(180^(\circ)-130^(\circ))=25^(\circ)`