How can I find 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
Gabe Rebs
2
0
IMG_20210228_150757.jpg

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
 

FAQ: How can I find angles in circles?

How do you find the measure of an angle in a circle?

To find the measure of an angle in a circle, you need to know the central angle and the radius of the circle. The measure of the angle is equal to the length of the arc it intercepts divided by the length of the radius, multiplied by 180 degrees.

What is the central angle of a circle?

The central angle of a circle is an angle whose vertex is at the center of the circle and whose sides pass through two points on the circle. It is measured in degrees and is equal to the arc length it intercepts divided by the radius of the circle.

How do you find the measure of an inscribed angle in a circle?

To find the measure of an inscribed angle in a circle, you need to know the measure of the central angle that intercepts the same arc as the inscribed angle. The measure of the inscribed angle is half of the measure of the central angle.

What is the relationship between an inscribed angle and a central angle in a circle?

The measure of an inscribed angle is always half of the measure of the central angle that intercepts the same arc. This relationship is known as the Inscribed Angle Theorem.

How do you find the measure of a tangent angle in a circle?

To find the measure of a tangent angle in a circle, you need to know the measure of the central angle that intercepts the same arc as the tangent angle. The measure of the tangent angle is equal to half of the difference between 180 degrees and the measure of the central angle.

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