Answer:
Part a) The measurement of arc KL is [tex]20\°[/tex]
Part b) The measurement of arc MJ is [tex]80\°[/tex]
Step-by-step explanation:
Let
x--------> the measure of arc KL
y-------> the measure of arc MJ
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
[tex]m<MEJ=\frac{1}{2}(y-x)[/tex]
substitute the given value
[tex]30\°=\frac{1}{2}(y-x)[/tex]
[tex]60\°=(y-x)[/tex]
[tex]y=60\°+x[/tex] ------> equation A
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
[tex]m<MFJ=\frac{1}{2}(x+y)[/tex]
substitute the given value
[tex]50\°=\frac{1}{2}(x+y)[/tex]
[tex]100\°=(x+y)[/tex]
[tex]y=100\°-x[/tex] ------> equation B
Equate the equation A and B and solve for x
[tex]60\°+x=100\°-x[/tex]
[tex]2x=100\°-60\°[/tex]
[tex]x=20\°[/tex]
Find the value of y
[tex]y=100\°-20\°=80\°[/tex]
therefore
The measurement of arc KL is [tex]20\°[/tex]
The measurement of arc MJ is [tex]80\°[/tex]
