Question

In the given figure, ABCD and BECD are parallelograms, BCFD is a rhombus. If `/_ DBC =80^(@), ` then which of the following are the angles of the triangle AEF ?
A. `60^(@),70^(@),50^(@)`
B. `60^(@),60^(@),60^(@)`
C. `50^(@),40^(@),90^(@)`
D. `50^(@),50^(@),80^(@)`

Answer 1

Correct Answer - d
BCFE is a rhombus and `/_ DBC =80^(@) ` (given) `implies /_ DFC = 80^(@)` and `/_ BDF =180^(@)-80^(@) =100^(@)`.
We know that the diagonals bisect the angles of rhombus.

`implies /_BDC = /_ BCD =(100^(@))/(2)=50^(@)`
`implies /_BEC =50^(@) ` ( opposite angle to `/_BDC` in the parallelogram BECD)
`implies /_ DAB =50^(@)` ( opposite angle to `/_ DCB ` in the parallelogram ABCD )
`:.` The angles of the triangle AEF are `50^(@),50^(@)` and `80^(@)`.