MHB How can I find angles in circles?

[Gabe Rebs]

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..

 

[HOI]

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.

 

[Gabe Rebs]

Thank You Very much :) I think I very much Understand Now