Answer:
m<FEG = 23°
m<FEH = 113°
Step-by-step explanation:
A diameter is always 180° to it's corresponding arc.
The circumference or full arc of a circle is 360°.
If EG is a diameter, Arc EG is 180°.
Given that Arc EF = 134°, and Arc EG = 180°.
Arc EF + Arc EG + Arc FG = 360°.
134° + 180° + Arc FG = 360°
314° + Arc FG = 360°
–314° –314°
Arc FG = 360° – 314° = 46°
The angle formed by the two chords that make the arc is ½ the measure of that Arc.
Meaning that m<feg which is the angle formed by arc FG is ½ 46° which means that m<feg = 23°.
Given that segment EH is tangent to point E.
The rule of a segment and a tangent is that the angle formed is also ½ the measure of the arc.
This means that m<FEH = ½(Arc FG + Arc EG)
m<FEH = ½(46° + 180°) = ½(226°) = 113°
