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Mathematics

1 answer:

Alexus [3.1K]3 years ago

5 0

Answer:

d. 89°

Step-by-step explanation:

The given measure of the angles formed are;

m∠AED = 48°, m $\widehat{AG}$ = 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 $\widehat{ABE}$ = 48°

∴ m $\widehat{ABE}$ = 2 × 48° = 96°

m∠AEF = (1/2) × m $\widehat{AGE}$

m $\widehat{ABE}$ + m $\widehat{AGE}$ = 360° (angle round a circle)

∴ m $\widehat{AGE}$ = 360° - m $\widehat{ABE}$ = 360° - 96° = 264°

m $\widehat{AGE}$ = m $\widehat{AG}$ + m $\widehat{EG}$

∴ m $\widehat{EG}$ = m $\widehat{AGE}$ - m $\widehat{AG}$ = 264° - 175° = 89°

m $\widehat{EG}$ = 89°.

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