Answer:
(a) ∠EFH = 68°
(b) ∠EGF = 21°
Step-by-step explanation:
(a) The given parameters are;
The diameter of the circle = Segment [tex]\overline{EG}[/tex]
Arc [tex]m\widehat{FG}[/tex] = 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 [tex]m\widehat{FG}[/tex] + Arc mEHG = 360 (Sum of angles at the center of a circle)
Arc mFE = 360 - ( Arc [tex]m\widehat{FG}[/tex] + 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°
