Answer:
d. 89°
Step-by-step explanation:
The given measure of the angles formed are;
m∠AED = 48°, m[tex]\widehat{AG}[/tex] = 175°
According to circle theorem, the angle formed by a chord and a tangent of a circle is given by half of the measure of the arc intercepted by the chord in the direction of the angle;
Therefore;
m∠AED = (1/2) × m[tex]\widehat{ABE}[/tex] = 48°
∴ m[tex]\widehat{ABE}[/tex] = 2 × 48° = 96°
m∠AEF = (1/2) × m[tex]\widehat{AGE}[/tex]
m[tex]\widehat{ABE}[/tex] + m[tex]\widehat{AGE}[/tex] = 360° (angle round a circle)
∴ m[tex]\widehat{AGE}[/tex] = 360° - m[tex]\widehat{ABE}[/tex] = 360° - 96° = 264°
m[tex]\widehat{AGE}[/tex] = m[tex]\widehat{AG}[/tex] + m[tex]\widehat{EG}[/tex]
∴ m[tex]\widehat{EG}[/tex] = m[tex]\widehat{AGE}[/tex] - m[tex]\widehat{AG}[/tex] = 264° - 175° = 89°
m[tex]\widehat{EG}[/tex] = 89°.
