Question

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

Answer 1

Answer:

Option (D). 129°

Step-by-step 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.