Solve for x. 5x + 20 = 70

Simplifying

5x + -20 = 70

Reorder the terms:

-20 + 5x = 70

Solving

-20 + 5x = 70

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.

-20 + 20 + 5x = 70 + 20

Combine like terms: -20 + 20 = 0

0 + 5x = 70 + 20

5x = 70 + 20

Combine like terms: 70 + 20 = 90

5x = 90

Divide each side by '5'.

x = 18

Simplifying

x = 18

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.