Question

Given: m

LJ
=4x+50°, m
KM
=6x
m
KL
=x+10°, m
MJ
=4x
Find: m∠MEJ

Answer 1

`m\angle MEJ=25^(\circ).`

Explanation:

The arcs LY, KM, KL and MJ together form the full revolution angle, thus

`4x+50^(\circ)+6x+x+10^(\circ)+4x=360^(\circ),\\ \\15x=300^(\circ),\\ \\x=20^(\circ).`

Note that

`m\angle MOJ=4x=80^(\circ),`

then

`m\angle MLJ=(1)/(2)\cdot 80^(\circ)=40^(\circ).`

So,

`m\angle ELM=180^(\circ)-40^(\circ)=140^(\circ).`

Also

`m\angle LOK=30^(\circ),`

so

`m\angle KML=(1)/(2)\cdot 30^(\circ)=15^(\circ).`

In triangle EML,

`m\angle MEL+m\angle EML+m\angle ELM=180^(\circ),\\ \\m\angle MEL=180^(\circ)-15^(\circ)-140^(\circ)=25^(\circ).`

Thus,
`m\angle MEJ=25^(\circ).`