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Nat2105 [25]
3 years ago
7

EB and DA are diameters of circle Y. What is the measure of arc EDC?

Mathematics
1 answer:
Dmitrij [34]3 years ago
4 0

Answer:

Option (D). 110°

Step-by-step explanation:

Since EB and AD are diameter,

m(\widehat{ECB}) = m(\widehat{ACD}) = 180°

m(\widehat{ECB})=m(\widehat{EDC})+m(\widehat{BC}) = 180° -------(1)

And m(\widehat{ACD})=m(\widehat{AB})+m(\widehat{BCD})

180° = 40° + m(\widehat{BCD})

m(\widehat{BCD}) = 140°

Since, m(\widehat{BCD})=m(\widehat{BC})+m(\widehat{CD})

2m(\widehat{BC}) = 140° [Given m(\widehat{BC})=m(\widehat{CD})]

m(\widehat{BC}) = 70°

From equation (1),

m(\widehat{EDC}}) = 180° - m(\widehat{BC})

m(\widehat{EDC}}) = 180°- 70°

Therefore, measure of arc(EDC) = 110°

Option (D) will be the answer.

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