In a circle of radius 10 cm, a sector has an area of 40 (pi) sq. cm. What is the degree measure of the arc of the sector? 72
144
180°

144°

Step-by-step explanation:

First, find the area of the circle, with the formula A = r²

Plug in 10 as the radius, and solve

A = r²

A = (10²)

A = 100

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:

=

Cross multiply and solve for x:

100x = 14400

x = 144

So, the degree measure of the sector arc is 144°

We know that

Area = πr²

Area = 3.14 × (10)²

Area = 314/100 × 100

Area = 314 cm²

Now

40π/314 = x/360

40 × 3.14/314 = x/360

125.6/314 = x/360

0.4 = x/360

0.4 × 360 = x

144 = x

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.