Question

plz hurry!!!! thank you!!!!

Answer 1

Answer:

$m\angle KLM=53.13^o$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

$KO=MO=r=5\ units$

$KM=8\ units$

Applying the law of cosines

$8^2=5^2+5^2-2(5)(5)cos(KOM)$

$64=50-50cos(KOM)$

$50cos(KOM)=50-64$

$50cos(KOM)=-14$

$cos(KOM)=-14/50$

$m\angle KOM=cos^{-1}(-14/50)$

$m\angle KOM=106.26^o$

step 2

Find the measure of the arc KM

we know that

$arc\ KM=m\angle KOM$ ----> by central angle

we have

$m\angle KOM=106.26^o$

so

$arc\ KM=106.26^o$

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising  

$m\angle KLM=\frac{1}{2}[arc\ KM]$

we have

$arc\ KM=106.26^o$

substitute

$m\angle KLM=\frac{1}{2}[106.26^o]$

$m\angle KLM=53.13^o$