Question

Given: measurement of arc LJ =4x+50°, measurement of arc KM=6x, measurement of arc KL=x+10°, measurement of arc MJ=4x.

Find: m∠MEJ

Answer 1

∠MEJ=25°

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°