Question

Identify the measure of arc BD.
A. 51
B. 72
C. 105
D. 129

Answer 1

Option (D). 129°

Explanation:

In the figure attached,

AB and CD are the diameters intersecting at the center of the circle F.

Central angle AFC = 129°

m(
`\widehat{AC}`) = 129°

m(∠AFD) = 180° - (m∠AFC)

= 180° - (129)°

= 51°

Since m∠AFD = m∠BFC = 51° [Vertical angles]

Therefore,
`m(\widehat{AD})=m(\widehat{BC})=51`

Now,
`m(\widehat{BC})+m(\widehat{BD})` = 180°

51° +
`m(\widehat{BD})` = 180°

`m(\widehat{BD})` = 180° - 51°

`m(\widehat{BD})` = 129°

Therefore, Option (D) will be the answer.