Question

Given: m

Answer 1

Answer:

$m\angle MEJ=25^{\circ}.$

Step-by-step 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

$m\angle MLJ=\dfrac{1}{2}\cdot 80^{\circ}=40^{\circ}.$

So,

$m\angle ELM=180^{\circ}-40^{\circ}=140^{\circ}.$

Also

$m\angle LOK=30^{\circ},$

so

$m\angle KML=\dfrac{1}{2}\cdot 30^{\circ}=15^{\circ}.$

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, $m\angle MEJ=25^{\circ}.$