Question

Please help ASAP!! question is in the image below

Answer 1

Answer:

(a) ∠EFH =  68°

(b) ∠EGF = 21°

Step-by-step explanation:

(a) The given parameters are;

The diameter of the circle = Segment $\overline{EG}$

Arc $m\widehat{FG}$ = 138°

∠GFH = 22°

∠ EFG = (Angle subtended by the diameter EG at the center)

Arc mEG = 180° (Arc subtended by the diameter of a circle = 180°)

∠ EFG is subtended by the diameter EG at the center

∴ ∠ EFG = 90° (Angle at the center = 2 times angle at the circumference)

∠EFG = ∠EFH + ∠GFH  (Angle addition postulate)

∴ ∠EFH = ∠EFG - ∠GFH = 90° - 22° = 68°

∠EFH =  68°

(b) ∠EGF

Arc GH = 44°

Arc mFE + Arc $m\widehat{FG}$ + Arc mEHG = 360 (Sum of angles at the center of a circle)

Arc mFE = 360 - ( Arc $m\widehat{FG}$ + Arc mEHG )

Arc mFE  =  360 - 180 - 138 = 42°

∠EGF = Arc mFE/2 (Angle at the center = 2 times angle at the circumference)

∠EGF = 42/2 = 21°

∠EGF = 21°