Finding Angles in Circles

In summary, the problem involves finding the measures of angles in a circle and using theorems related to isosceles triangles and angles subtended by arcs on the circle. For angle 1 and 2, the measure is 30 degrees and for angle 3, it is 45 degrees. The theorems state that an angle with vertex on the circle has an arc measure twice the angle measure, and an angle with vertex at the center of the circle has an arc measure equal to the angle measure.
  • #1
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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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  • #2
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.
 
  • #3
Thank You Very much :) I think I very much Understand Now
 

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