Question

Given: circle k(O),

m

JC

= 94°

Find: m∠LJC

Answer 1

The measure of angle LJC is
`m\angle LJC=43\°`

Explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc LC

we know that

`arc\ LC+arc\ JC=180\°` ----> because the diameter divide the circle into two equal parts

substitute the given values

`arc\ LC+94\°=180\°`

`arc\ LC=180\°-94\°=86\°`

step 2

we know that

The inscribed angle measures half that of the arc comprising

so

`m\angle LJC=(1)/(2)[arc\ LC]`

substitute

`m\angle LJC=(1)/(2)[86\°]=43\°`