Answer:
The measure of angle EYL is [tex]45\°[/tex]
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
Let
x-----> the measure of arc EVL
y----> the measure of arc EHL
[tex]m<EYL=\frac{1}{2}(x-y)[/tex]
[tex]m<EYL=\frac{1}{3}(y)[/tex]
so
[tex]\frac{1}{3}y=\frac{1}{2}(x-y)[/tex]
Multiply by 6 both sides
[tex]2y=3x-3y[/tex]
[tex]3x=5y[/tex]
[tex]x=\frac{5}{3}y[/tex] -----> equation A
[tex]x+y=360\°[/tex] -----> equation B ( is a complete circle)
substitute equation A in equation B
[tex]\frac{5}{3}y+y=360\°[/tex]
[tex]\frac{8}{3}y=360\°[/tex]
[tex]y=(360\°)*(3)/8=135\°[/tex]
Find the value of x
[tex]x=\frac{5}{3}(135\°)=225\°[/tex]
Find the measure of angle EYL
[tex]m<EYL=\frac{1}{2}(x-y)[/tex]
substitute the values
[tex]m<EYL=\frac{1}{2}(225\°-135\°)=45\°[/tex]
