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

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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