Question

AB, CA and EF are three concurrent lines passing through the point O such that OF bisects angle BOD . if angle BOF=35,find angleBOC and angleAOD

Answer 1

in this question the lines must be AB, CD and EF..hope my solution is helpful

Answer 2

Step 1:  Given we have three concurrent lines passing through the points ‘O’ and OF bisect angle BOD

Step 2:  <BOF = $35^{0}$

Step 3: < OF bisect <BOD

<BOF = < FOD = ½ <BOD =$35^{0}$ (given <BOF = $35^{0}$)

Step 4:  We know sum of all angles on a line is $180^{\circ}$

<BOF + <FOD + <AOD = $180^{\circ}$

35 + 35 + <AOD = $180^{\circ}$

<AOD=180-70

<AOD=110

Step 5:  <AOD and <BOD are opposite angles as formed by two line AB and CD and we know opposite angles are equal  

Step 6:  <AOD = <BOC

So <BOC = $110^{\circ}$