Question

An artist used this design to create a stained glass window. If m∠M = 48° and

Answer 1

Answer:

$m\angle LKM=36^o$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of arc KN

we know that

The inscribed angle is half that of the arc comprising

so

$m\angle M=\frac{1}{2}(arc\ KN)$

we have

$m\angle M=48^o$

substitute

$48^o=\frac{1}{2}(arc\ KN)$

$arc\ KN=96^o$

step 2

Find the measure of arc LM

we know that

$arc\ KN=arc\ MN=arc\ KL=96^o$

so

$3arc\ KN+arc\ LM=360^o$ ----> by complete circle

substitute given value

$3(96^o)+arc\ LM=360^o$

$arc\ LM=360^o-288^o=72^o$

step 3

Find the measure of angle LKM

we know that

The inscribed angle is half that of the arc comprising

so

$m\angle LKM=\frac{1}{2}(arc\ LM)$

substitute the given value

$m\angle LKM=\frac{1}{2}(72^o)=36^o$