Question

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

Answer 1

Option (D). 110°

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.