Find the measure of each angle using the triangle sum theorem and exterior angle theorem

(please open my photo for reference as you read, I am a visual learner/explainer so it will make the most sense that way)

So the first thing you want to do is look at the exterior angle 130°. A straight line is 180°, and every Triangle's angular sum is 180°. How I think of it is that every straight line has a mini protractor on either side. It makes it a bit easier to understand.

180 - 130 = 50

You now know that two of the angles are 50°.

You now have two of the measurements for the triangle farthest to the left.

75° and 50°

75 + 50 = 125

180 - 125 = 55

a = 55°

Now that you have all the measurements for the first triangle, let's move onto the next one.

With two measurements for the second triangle, all you need to do is find their sum and subtract that from 180 and you will have the third measurement!

50 + 60 = 110

180 - 110 = 70

b = 70°

Finally, for the last triangle, you already have two of the measurements 60° and 85°.

85 + 60 = 145

180 - 145 = 35

c = 35°

Sorry if this explanation is a bit messy, it's hard to describe certain things without a letter or some kind of name to differentiate between them verbally.

I hope this helps! <3

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)