Answer:
∠MEJ=25°
Step-by-step explanation:
step 1
Find the value of x
we know that
arc LJ+arc KM+arc KL+arc MJ=360° ----> complete circle
substitute the values
(4x+50)°+6x°+(x+10)°+4x°=360°
solve for x
(15x+60)°=360°
x=300°/15=20°
step 2
Find the measure of angle MEJ
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
∠MEJ=(1/2)[arc MJ-arc KL]
arc MJ=4(20°)=80°
arc KL=20°+10°=30°
substitute the values
∠MEJ=(1/2)[80°-30°]=25°
