We appreciate your visit to if the measure of arc CDE 118 degrees and the measure of arc EF 62 degrees calculate measure of angle FGE. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
The measure of angle FGE from the given figure is 28°.
Given that, the measure of arc CDE = 118° and the measure of arc EF = 62°.
The measure of an arc is equal to the measure of its corresponding central angle.
From the given figure, the measure of arc CDE = 118° = corresponding central angle (∠CAE)
So, ∠CAE = 118°
From the given figure, the measure of arc FE = 62° = corresponding central angle (∠FAE)
So, ∠FAE = 62°
As we know the radius of a circle is perpendicular to the tangent.
That is, AE ⊥ EG
So, ∠AEG = 90°
Now, ∠AGE+∠AEG+∠GAE = 180° (The sum of interior angles of a triangle is equal to 180°)
∠AGE + 90° + 62° = 180°
⇒ ∠AGE + 152° = 180°
⇒ ∠AGE = 28°
So, ∠AGE = ∠FGE = 28°
Therefore, the measure of angle FGE from the given figure is 28°.
To learn more about the arc length visit:
https://brainly.com/question/16403495.
#SPJ1
Thanks for taking the time to read if the measure of arc CDE 118 degrees and the measure of arc EF 62 degrees calculate measure of angle FGE. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
Rewritten by : Barada
The angle FGE will be equal to 28 degrees.
The phrase "the intersecting chords theorem" refers to a relationship between the four-line segments formed by two intersecting chords inside of a circle. The products of the line segment lengths on each chord, according to this statement, are equal.
Given that if the measure of arc CDE=118 degrees and the measure of arc EF=62 degrees. The angle FGE will be calculated as:-
Angle CDE=118 then the angle AFE will be:-
AFE = 180 - 118 = 62
From the angle of chord theorem angle EBF = 31. Now the angle AFE and AEF will be 59 degrees. Angle GEF will be 31 degrees and angle EFG will be 121 degrees by supplementary property.
Angle EGF = 180 - 121 - 31 = 28
Therefore, the angle FGE will be equal to 28 degrees.
To know more about the angle of chords theorem follow
https://brainly.com/question/23732231
#SPJ1
