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3 years ago

What would be the measure of arc DF, DEB, and BEC?? Thanks!!

Mathematics

1 answer:

olga2289 [7]3 years ago

6 0

Answer:

Part A) The measure of arc DF is 129°

Part B) The measure of arc DEB is 270°

Part C) The measure of arc BEC is 321°

Step-by-step explanation:

Part A) What would be the measure of arc DF?

we know that

CF is a diameter

The measure of arc CDEF is equal to 180 degrees

arc CD+arc DE+arc EF=180°

substitute the given values

51°+90°+arc EF=180°

arc EF=180°-(51°+90°)=39°

arc DF=arc DE+arc EF

arc DF=90°+39°=129°

Part B) What would be the measure of arc DEB?

we know that

arc DEB=arc DE+arc EFB

we have

arc DE=90°

arc EFB=180° -----> because EB is a diameter

substitute

arc DEB=90°+180°=270° -----> 3/4 of a circle

Part C) What would be the measure of arc BEC?

we know that

arc BEC=arc DEB+arc CD

we have

arc DEB=270°

arc CD=51°

substitute

arc BEC=270°+51°=321°

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