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tigry1 [53]
3 years ago
8

NEED THE ANSWER PLEASE

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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