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kondaur [170]
3 years ago
6

Given: m

Mathematics
1 answer:
Nutka1998 [239]3 years ago
7 0

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}.

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