Answer:
The measure of angle EYH is [tex]25\°[/tex]
Step-by-step explanation:
step 1
Find the measure of arc EH
we know that
[tex]arc\ EV+arc\ VL+arc\ HL+arc\ EH=360\°[/tex] ----> by complete circle
substitute the given values
[tex]130\°+110\°+40\°+arc\ EH=360\°[/tex]
[tex]280\°+arc\ EH=360\°[/tex]
[tex]arc\ EH=360\°-280\°=80\°[/tex]
step 2
Find the measure of angle EYH
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
[tex]m<EYH=\frac{1}{2}(arc\ EV-arc\ EH)[/tex]
substitute the values
[tex]m<EYH=\frac{1}{2}(130\°-80\°)=25\°[/tex]
