Question

Assume that lines which appear tangent are tangent

Answer 1

Answer:

b

Step-by-step explanation:

360-244/2= 116/2=58 or b

Answer 2

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