SOLUTION: Can you tell me if my answers are correct. Bonus 1 and 2 https://answers.yahoo.com/question/index?qid=20200224171810AA3koFV

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Question 1152926: Can you tell me if my answers are correct. Bonus 1 and 2
https://answers.yahoo.com/question/index?qid=20200224171810AA3koFV
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
The other four parts of the arc add to 256 degrees.
What is left is 104 degrees, which is the missing arc and answer.
The angle needed is half of that 104 degrees (inscribed angle) or 52 degrees.

Answer by greenestamps(13208) (Show Source):
You can put this solution on YOUR website!

Here are the things you need to answer all of these questions....

(I) Arc measures can be added; and the sum of the measures of all the arcs in a circle is 360 degrees.
(II) The sum of the measures of the angles of a linear pair (e.g., angles 4 and 5) is 180 degrees.
(III) The measure of the angle formed by two tangents and/or secants from a point OUTSIDE the circle is half the DIFFERENCE of the measures of the two arcs cut off by the tangents or secants.
(IV) The measure of the angle with a vertex ON the circle is half the measure of the arc cut off by the two sides of the angle. This applies if the two sides of the angle pass through the circle or if one (or even both!) of the sides of the angle are tangent to the circle.
(V) The measure of the angle formed by two chords of a circle is half the SUM of the two arcs cut off by the two chords.

1) measure of arc BF: Using (I), your idea for getting the answer is right; but you left arc DE out of your calculation.

2) measure of arc BDF: ditto....

3) angle 1: use (III) -- the two arcs are BDF and BF (from questions 1 and 2)

4) arc BFC: use (I) -- the whole circle, minus arc BC

5) angle 2: use (IV) -- the arc cut off by angle 2 is arc BFC (from question 4)

6) angle GBC: use (II) -- linear pair with angle 2 (from question 5)

7) arc BFE: use (I)

8) angle 3: use (IV) -- the arc it cuts off is BFE (from question 7)

9) angle 4: use (V) -- the two chords cut off are CD and EF

10) angle 5: use (II) -- linear pair with angle 4 (from question 9)

11) arc FBC: use (I)

12) angle 6: use (III) -- the two arcs cut off are FBC (from question 11) and EF

13) arc FBD: use (I)

14) angle 7: use (IV) -- the arc cut off is FBD (from question 13)

15) angle 8: use (III) -- the two arcs are BF and CD