Answer:
a) 45
b)135
Step-by-step explanation:
[tex]In\ order\ to\ find\ the\ sum\ of\ all\ the\ interior\ angles\ of\ a\ polygon\ with\ sides\ n,\\S=180(n-2)\\Here,\\As\ the\ figure\ is\ a\ regular\ octagon\ ,\\The\ sum\ of\ all\ of\ its\ angles\ = 180(8-2)\\=180*6=1080\\Hence,\\Given\ that\ it\ is\ regular\ or\ that\ all\ of\ its\ angles\ are\ equal\ in\ measure.\\Hence,\\b) Angle\ ABC=1080/8\\=135\\As\ it\ is\ regular\ , the\ diagonals\ passing\ through\ the\ center\ bisects\ the\ respective\ angles.[/tex]Hence,
[tex]Angle OAB=135/2 = 67.5\\Angle ABO=135/2=67.5\\Through\ the\ angle\ sum\ property\ of\ a\ triangle\\Angle OAB+AngleABO+Angle AOB=180\\67.5+67.5+AngleAOB=180\\135+AngleAOB=180\\Angle AOB=180-135\\=45[/tex]
