Question

if the bisectors of Angle B and angle C of triangle ABC meet at point O then prove that angle BOC is equal to 90 degree + half angle A

Answer 1

Answer:

Step-by-step explanation:

To prove angle BOC = 90°+1/2 angle a

Proof: In triangle ABC

angle a+ angle B + angle c = 180° ( by angle sum property)

angle a + 2angle OBC+ 2angle ocb =180°

2( angle OBC+ angle ocb) =180°-angle a

angle obc + angle ocb = 180°/2-angle a/2

angle obc + angle ocb = 90°- a/2

Now in triangle BOC

angle boc + angle obc + angle ocb = 180° ( by angle sum property)

angle boc = 180° - ( angle obc+ angle ocb)

angle boc = 180° - (90°-angle a/2)

angle boc = 180°-90°+angle a/2

angle boc = 90°+angle a/2

H.P.