## Trying to find an angle in lines layed on top of a circle

1. The problem statement, all variables and given/known data
The problem is attached as TheProblem.jpg and the answer is A.

2. Relevant equations
Geometry rules.

3. The attempt at a solution
The triangle which has angles of 30deg and 10deg also has an angle of 180deg-30deg-10deg = 140deg and the other side of the line intersection “scissor” is also 140deg. The two equivalent angles on the other part of the line intersection “scissor” are (360deg-2*140deg)/2 = 40deg. I don't know if what I did so far is even useful nor do I know how to proceed from here.

Any help would be greatly appreciated!
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 First try and identify what arcs you need to know the measure of to find angle ACE. What formula are you going to ultimately use?
 I'm really unsure but (1) arc AE and (2) comparing an angle ratio with an arc/circumference ratio?

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## Trying to find an angle in lines layed on top of a circle

Have you learned "If AB and CD are lines intersecting inside a circle, then the angle between them is the average of the two arcs they make on the circle"? That is the theorem you need.
 HallsofIvy, did you mean "difference" instead of "average"? Because, if you did, then I get the correct answer by doing: angle A0E = 2 * angle ABE = 2 * 30deg = 60deg then angle ACE = 1/2 * (60-10) deg = 25deg

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 Quote by s3a 1. The problem statement, all variables and given/known data The problem is attached as TheProblem.jpg and the answer is A. 2. Relevant equations Geometry rules. 3. The attempt at a solution The triangle which has angles of 30deg and 10deg also has an angle of 180deg-30deg-10deg = 140deg and the other side of the line intersection “scissor” is also 140deg. The two equivalent angles on the other part of the line intersection “scissor” are (360deg-2*140deg)/2 = 40deg. I don't know if what I did so far is even useful nor do I know how to proceed from here. Any help would be greatly appreciated! Thanks in advance!
Consider the chord BD (and the minor arc BD). What can you say about the relationship between the angles BOD and BED?

That should take you most of the way.

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