Question

BRAINLIEST IF ANSWERED 

Answer 1

Answer:

The measure of angle K=25°.

Step-by-step explanation:

It is given that ΔKNM is an isosceles triangle with KL=LM and ∠K=∠M, and  NL bisects ∠KNM, thus

∠KNL=∠LNM

⇒5x+10=6x-1

⇒x=11°

Thus, ∠KNM=∠KNL+∠LNM

∠KNM=5x+10+6x-1=11x+9=11(11)+9=130°

Now, Since, ∠K=∠M,using the angle sum property in ΔKNM is an isosceles triangle with KL=LM and ∠K=∠M, and  NL bisects ∠KNM, thus, we get

∠NKM+∠KNM+∠KMN=180°

⇒2∠NKM+130°=180°

⇒2∠NKM=50°

⇒∠NKM=25°

Thus, the measure of angle K=25°.

Answer 2

we know that

An isosceles triangle has two equal sides and two equal angles

so

KN=NM

∠K=∠M

The line NL bisect the triangle KNM

therefore

$5x+10=6x-1$

Solve for x

$6x-5x=10+1$

$x=11\°$

Find the measure of angle N

∠N=$5x+10+6x-1$

substitute the value of x

∠N=$5*11+10+6*11-1=130\°$

Find the measure of angle K

∠N+∠K+∠M=$180\°$

remember that

∠K=∠M

∠N+2∠K=$180\°$

substitute the values and solve for ∠K

∠K=$\frac{1}{2}(180\°-130\°)=25\°$

therefore

the answer is the option

the measure of angle K is $25\°$