The three angles of a triangle form an A. P. If the largest angle is twice than the smallest angle find theee angles of that triangle

Let the angles be (a-d), a , (a+d)

a-d + a + a + d = 180 (angle sum property)

3a = 180

a = 60

Given:

a+d = 2(a-d)

60 + d = 2(60 - d)

60 + d = 120 - 2d

3d = 120 - 60

d = 20

Angles are : 40 , 60 , 80

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.

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn