Question

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

Answer 1

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.