Question

How to do this question plz answer ​

Answer 1

a) 45

b)135

Explanation:

`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.`Hence,

`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`

Answer 2

Explanation:

a) m∠AOB = 360°/8 = 45°

Internal angle is 360°, divided by 8 sides of octagon

b) m∠ABC = 2m∠ABO

m∠ABO = m∠BAO = 1/2(180° - 45) = 1.2(135°)

m∠ABC = 2*1/2(135°) = 135°