Question

The bisectors of angle B and angle C intersect each other at a point O. Prove that angle BOC=90°+1/2 angle A

Answer 1

Step-by-step explanation:

In Triangle OBC the angles

OBC = 1/2 (BAC + BCA)

OCB = 1/2 (BAC + CBA)

By angle sum property

BOC = 180 - 1/2 (BAC +BAC+ BCA + CBA)

BOC = 180 - 1/2 (BAC + 180)

BOC = 180 - 90 - 1/2 BAC

BOC = 90 - 1/2 BAC