Question

Q.3 In the given figure, bisectors of angleABC and 4 BCA intersect each other at O. If angleBAC =
50° Find BOC.​

Answer 1

Answer:

Since OB bisects <ABC,

<OBC=<OBA

Now,

<OBC+<OBA=<ABC

⇒<OBC+<OBC=<ABC(<OBC=<OBA)

⇒<ABC=2<OBC ...(1)

Similarly,since OC bisects <ACB,

<ACB=2<OCB ...(2)

In triangle ABC,

<BAC+<ABC+<ACB=180º(Angle sum property)

⇒50º+≺ABC+<ACB=180º(Given:<BAC=50º)

⇒<ABC+<ACB=130º

From eq.(1) and eq.(2),

2<OBC+2<OCB=130º

⇒2(<OBC+<OCB)=130º

⇒<OBC+<OCB=65º ...(3)

Now, in triangle BOC,

<OBC+<OCB+<BOC=180º(Angle sum property)

From eq.(3),

65º+≺BOC=180º

⇒<BOC=115º.

(Note:- While writing in N.B., please use the proper sign for angle)

Answer 2

Answer:

this is the right answer