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
so
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°
