Question

In figure, BO and CO are the bisectors of angle DBCand angle ECBrespectively.IfangleBAC =50° andangle ABC = 60°, then find the measure of angle BOC.

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Answer 1

Answer:

in ∆ ABC, |C = 180 - (|A + |B)

|C = 180 - ( 50° + 60° )

therefore. |C = 70° [ angle sum property of∆ ]

|DBC = 180 - |B

= 180 - 60° = 120° [ linear pair ]

since BO is the angle bisector of |DBC,

|DBO = |OBC = 120°/2 = 60° ...........(1)

similarly |ECB = 180 - |C = 180 - 70 = 110°

again as CO is the angle bisector of |ECB,

|ECO = |OCB = 110°/2 = 55° .....,......(2)

now in ∆ BOC, |OBC + |OCB + |BOC = 180°.....(3)

[ angle sum property ]

from (1) |OBC = 60° and from (2) |OCB = 55°

putting these values in (3)

60° + 55° + |BOC = 180°

therefore |BOC = 180-(60+55)

=> |BOC = 180° - 115°

=> |BOC = 65° Answer