Question

Bisector of the exterior angle B and C formed by producing sides AB and AC of triangle ABC intersect each other

Answer 1

Answer:

Step-by-step explanation:

In triangle BOC,

< BOC = 108' - (<CBO = <BCO).........( angle sum property of a triangle)

<BOC =180' - (x+y)

x + y = 180' - <BOC .......(1)

Using exterior angle property

<CBD = <A + <ACB .......(2)

Now, <ACB = 180' - <BCE

<ACB = 180' - 2x ....(3)

Substitute (3) in (2), we get,

<CBD = < A + 180' - 2x

2y = <A = 180' - 2x

2(x+y) = <A + 180'

x+y = 1 divided by 2 <A + 90'

180' - <BOC = 1 divided by 2 < A + 90'

<BOC = 90' - 1 divided by 2 <A