Answer:
144°
Step-by-step explanation:
First, find the area of the circle, with the formula A = [tex]\pi[/tex]r²
Plug in 10 as the radius, and solve
A = [tex]\pi[/tex]r²
A = [tex]\pi[/tex](10²)
A = 100[tex]\pi[/tex]
Using this, create a proportion that relates the area of the sector to the degree measure of the arc.
Let x represent the degree measure of the arc of the sector:
[tex]\frac{40\pi }{100\pi }[/tex] = [tex]\frac{x}{360}[/tex]
Cross multiply and solve for x:
100[tex]\pi[/tex]x = 14400[tex]\pi[/tex]
x = 144
So, the degree measure of the sector arc is 144°
