Question

The bisector BO and CO of
angle CBE and angle BCD respectively meet at O, then prove that
angleBOC=90degree- 1/2 angleBAC

Answer 1

Ray BO is the bisector of angle CBE.
Therefore, angle CBO = 1/2 angle CBE
= 1/2 (180°-y)
= 90°-y/2--------------> (1)

Similarly, Ray CO is the bisector of angle BCD
Therefore, angle BCO = 1/2 angle BCD
=1/2(180°-z)
= 90°-z/2---------> (2)

In ∆BOC, angle BOC + angle BCO + angle CBO = 180° -------------> (3)
substituting (1), (2) and (3)
angle BOC +90°-z/2+90°-y/2 = 180°
angle BOC = z/2+y/2 --------------> (4)
angle BOC = 1/2(y+z) ( angle sum property)
Therefore, (4) becomes
angle BOC = 1/2 (180°-x)
=90°-x/2
=90°-1/2 angle BAC

Hope this helps you friend
Thanks ✌️✌️

Answer 2

Hey mate!!!

Answer refer to the attachment


hope it helps a little!!!