Given that ab is a diameter of circle o, find the missing angle arc measures.

Part 1)

Part 2)

Part 3)

Part 4)

Part 5)

Step-by-step explanation:

Part 1) Find the measure of arc CB

we know that

-----> by central angle

we have

----> given problem

so

Part 2) Find the measure of angle AOC

we know that

------> by supplementary angles

we have

substitute

Part 3) Find the measure of arc AD

we know that

The inscribed angle measures half that of the arc comprising

so

we have

substitute

Part 4) Find the measure of arc DFB

we know that

we have

-----> because is a diameter

substitute

Part 5) Find the measure of angle CDB

we know that

The inscribed angle measures half that of the arc comprising

so

we have

substitute

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft