Question

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

arc MN = arc KN = arc KL , what is m∠LKM?

Answer 1

`m\angle LKM=36^o`

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=(1)/(2)(arc\ KN)`

we have

`m\angle M=48^o`

substitute

`48^o=(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=(1)/(2)(arc\ LM)`

substitute the given value

`m\angle LKM=(1)/(2)(72^o)=36^o`