Question

given that AOB and COD are straight lines, find the value(s) of the unknown(s) in each of the following figures.​

please write full explanation/working

Answer 1

Answer:

Given

COD is a straight line

COB+BOD=180°(adjacent angles are supplementary)

117+BOD=180

BOD=180-117

BOD=63°

Also

AOC=BOD(vertically opposite angles are equal)

AOC=63°

or else you can use

AOC+BOC=180(adjacent angles)

AOC+117=180

AOC=180-117

AOC=63°

and Now

we've AOB is a straight line

that is

BOD+DOF+FOE+EOA=180°

63+40+30+a°=180°

133+a=180

a=180-133

a=47°

that is

EOA=47°

So the angles are

COB=117°

BOD=63°

DOF=40°

FOE=30°

EOA=47°

AOC=63°

for checking they are correct or not

we've to use

COB+BOD+DOF+FOE+EOA+AOC=360°(sum of all angles meeting at a point)

117+63+40+30+47+63=360°

360=360

L.H.S=R.H.S

hence verified

hope it helps