Answers

  • Brainly User
2014-09-13T14:24:14+05:30
Angle BOC  = 180 - (Angle CBO + Angle BCO) ----(1)

Since exterior angle of a triangle equal the sum of opposite interior angles, we have:-
Angle CBO = (1/2) angle CBP(Ext. angle)  = (1/2) (Angle A + Angle C)
Angle BCO = (1/2) angle BCQ (Ext. angle) = (1/2) (angle A + angle B)

==> angle CBO + angle BCO
       = (1/2)[(angle A+angleC) + (angle A + angle B)]
       = (1/2)[ (angle A + angle B + angle C) + angle A]
       = (1/2) ( 180 + angle A) = 90 + (1/2) angle A  ------(2)

From (1) and (2),
Angle BOC = 180 - [90 + (1/2) angle A] = 90 - (1/2) angle A
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