Please help me The measure of an exterior angle of a triangle is 40°. What is the sum of the measures of the corresponding remote interior angles?

40 degrees

Step-by-step explanation:

Because there are 180 interior angles in a triangle, you need one of the sides. If an angle's exterior is 40 degrees, we know that the interior angle is 140 degrees. This means that the sum of the other interior angles have to be 40 as 180-140 is 40.

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.

at least two

step-by-step explanation: