MHB How can I find angles in circles?

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To find angles in circles, understanding the properties of isosceles triangles formed by radii is crucial, as they indicate that angles at the base are equal. For example, if angles 1 and 2 are both 30 degrees, then angle FOW is calculated as 120 degrees. The relationship between angles and arcs is governed by the theorem stating that an angle with its vertex on the circle subtends an arc that measures twice the angle. Similarly, if angle 1 is 40 degrees, angle FOW would be 100 degrees, demonstrating that the angle at the center equals the arc it subtends. This foundational knowledge aids in solving various angle-related problems in circles.
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Please Help.. I am struggling to answer this inspite of trying to re read theorems.. I couldn't answer anything.. if you can solve this please teach me the steps.

So i could answer them in the future..
 
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Since OF and OW are radii or the circle, they have the same length and OFW is an isosceles triangle. That means that angle 1 and angle 2 have the same measure so, in 1, angle 2 is also 30 degrees. Now there is a theorem that says that an angle with vertex on the circle subtends an arc with measure twice the measure of the angle. If angles 1 and 2 have measure 30 degrees then angle FOW has measure 180- 30- 30= 120 and angle 3 is the "supplement" of that.

For 2, if angle 1 has measure 40, so does angle 2 so angle FOW has measure 180- 40- 40= 100. There is a theorem that says that an angle with vertex at the center of the circle subtend an arc with measure equal to the measure of the angle.

3 is exactly the same as 1 except you are to us 45 degrees instead of 30 degrees.
 
Thank You Very much :) I think I very much Understand Now
 

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