Reme has drawn an isosceles triangle ABC whose included angle of two equal sides is `angleABC=45^(@) , "the bisector of angleABC intersects the side AC at the point D. Determine the circular values of" angleABD,angleBAD,angleCBD,and angleBCD`

Explanation

Let BD is the bisector of `angle ABC` which intersects the sides AC at D.
`therefore angleABD=(1)/(2)angleABC=(1)/(2)xx45^(@) [therefore angleABC=45^(@)]`
`=(1)/(2)xx45^(@)xx(pi)/(180^(@))=(pi)/(8)`
`angleBAD=90^(@)-angleABD`
`=90^(@)-(45^(@))/(2)=(180^(@)-45^(@))/(2)`
`=135^(@)/(2)xx(pi)/(180^(@))=(3pi)/(8)`
`[therefore BD "is the bisector of" angleABC and AB =BC, therefore BD bot AC` and
`angleADB=90^(@)]`
`angleCBD= angleABD=(pi)/(8).`
`angleBCD =angleBAD [because BA=BC,therefore angleBCD=angleBAD]=(3pi)/(8).`
Hence the required angles are `(pi)/(8),(3pi)/(8),(pi)/(8),(3pi)/(8)` respectively.