Answer:
B
Step-by-step explanation:
Remark
This is a monster when you first come across it, but later on you will not be fooled.
Construction
- Draw a line from E to the center of the circle.
- Label the center of the circle O
- OE and OF are both radii.
- They form the central angle of the ArcEF
Solution
Find the value of Arc EF
The value of Arc EF = 360 - 244 = 116
The value of <FOE also = 116. (The arc and the central angle are equal.)
ΔFOE = 116 degrees See above statement
ΔFOE is isosceles Two of it's sides are radii.
The two base angles can be solved. Call each one x
2x + 116 = 180 All triangles have 180 degrees
-116 -116 Subtract 116 from both sides
2x = 64 Divide by 2
x = 32 <EFO = 32
<EFO = 90 Where the tangent meets the radius forms a 90o angle.
<EFO + GFE = 90
32 + GFE =90
GFE = 90 - 32
GFE = 58
Answer: B
