1 Answer

Bddicken · Answer 1 · 2020-03-31T06:04:39+0000

Answer:

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

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

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