The measure of the exterior angle of the triangle is ___

114°

Step-by-step explanation:

Here, we need to know the idea of the "Exterior Angle theorem".

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.

If you are still confused, then refer to the attachment below for a graphical explanation.

Given

24 + (2x + 18) = 3x + 6

Put like terms together

24 + 18 + 2x = 3x + 6

Combine like terms

42 + 2x = 3x + 6

Subtract 6 on both sides

42 + 2x - 6 = 3x + 6 - 6

36 + 2x = 3x

Subtract 2x on both sides

36 + 2x - 2x = 3x - 2x

x = 36

Exterior angle = 3x + 6 = 3(36) + 6 = 114°

Hope this helps!! :)

Please let me know if you have any questions

Exterior angle

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.