Question

NEED THE ANSWER PLEASE

Answer 1

d. 89°

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°.