In the above figure, `GH ||IJ` and `AC || BD, AB` and CD are bisectors of `/_ EAH` and `/_ FCJ` respectively. Find the `/_ ABD +/_ BDC `, if `/_ BAC= 3/_ BDC`.

Options

A. `80^(@)`
B. `90^(@)`
C. `100^(@)`
D. `110^(@)`

Answer

b

Explanation

(i) Sum of the angles in a straight line is `180^(@)`. Vertically opposite angles are equal. Co-interior angles are supplementary .
(ii) Let `/_ FCD = /_ DCJ =x^(@)` and `/_EAB= /_BAH =y^(@)`.
(iii) `/_BDC =/_ DCF` (alterante angles ) and `/_ BAC = 3 /_ BDC` (1) (given)
(iv) `/_ ACJ =(180^(@)) = (180^(@) - 2 x^(@))`
`:. /_ HAC = /_ EAH` (2)
(vi) Solve equations (1) and (2) .