20 points brainlist thanks please help Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)

<x = 53 degrees

Step-by-step explanation:

<Q = 62 degrees (alternate angle)

<PRQ = 180-115 (Angles on a straight line add up to 180 degrees)

<PRQ = 65 degrees

Now, Finding <x

To find <x, we'll simply subtract 180 from rest of the triangles interior angles because the interior angles of a triangle add up to 180 degrees

=> <x = 180-65-62

=> <x = 53 degrees

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.

the balance is found at the link

step-by-step explanation: