Find the measure of YVZ

47°

Explanation:

Line UVW is a straight line. This means it must have a measure of 180°. As you can see in the diagram, <UVX, <XVY, <YVZ, and <ZVW also split <UVW into four different angles. By this logic, we know:

<UVX +  <XVY + <YVZ + <ZVW = 180°

Now, let's add in the values of the known angle measures and let x represent <YVZ in this equation:

43 + 52 + x + 38 = 180

133 + x = 180

x = 47

So, m<YVZ = 47°.

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.

can you put the picture up?

step-by-step explanation: