Q. 74.3( 22 Votes )

ABC is a triangle in which A = 72°, the internal bisectors of angles B and C meet in O. Find the magnitude of BOC.

Answer :

Given,

ABC is a triangle


A = 72o and internal bisectors of B and C meet O.


In


A + B + C = 180o


72o + B + C = 180o


B + C = 180o – 72o


B + C = 108o


Divide both sides by 2, we get


+ =


+ = 54o


OBC + OCB = 54o (i)


Now, in


OBC + OCB + BOC = 180o


54o + BOC = 180o [Using (i)]


BOC = 180o – 54o


= 126o


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