Answer:
The measures of the intercepts arcs are [tex]58\°[/tex]  and [tex]122\°[/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,y -----> the intercepts arcs
[tex]x+y=180\°[/tex] ----> equation A
[tex]32\°=\frac{1}{2}(x-y)[/tex]
[tex]64\°=(x-y)[/tex]
[tex]x=64\°+y[/tex] ------> equation B
substitute equation B in equation A
[tex](64\°+y)+y=180\°[/tex]
[tex]64\°+2y=180\°[/tex]
[tex]2y=180\°-64\°[/tex]
[tex]y=116\°/2=58\°[/tex]
Find the value of x
[tex]x=64\°+58\°=122\°[/tex]
therefore
The measures of the intercepts arcs are [tex]58\°[/tex]  and [tex]122\°[/tex]
