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

Identify the measure of arc BD. A. 51 B. 72 C. 105 D. 129-example-1

1 Answer

3 votes

Answer:

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.

User Randy Simon
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