Answer:
B=100
Step-by-step explanation:
The given circle is
Consider the triangle AOB, Using the triangle sum property, we get
AOB+AOB+BOA=180
Substitute ABO=55 and BAO=45 we get
AOB+55+45=180
AOB+100=180
AOB+100-100=180-100
AOB=80
Here AOB and AOC are supplementary angles
The sum of the supplementary angles is 180 degrees.
AOB+AOC=180
Substitute AOB=80 we get
80+AOC=180
80+ AOC-80=180-80
AOC=100
Now consider the Central angle AOC and intercepted arc AC.
mAOC=mAC
Substitute m AOC=100 and mAC=b we get
100=b
Hence the value of b is 100 degrees.
