# In a quadrilateral ABCD, <ABC=40, <BCD=100 and <CDA=60. E is a point on BC such that AE bisects the angle BAD. Find the size of the angle AED if <BCA=44.

*print*Print*list*Cite

### 1 Answer

We are given `m/_B=40,m/_C=100,m/_D=60` so since this is a quadrilteral `m/_A=80` .

`bar(AE)` bisects `/_BAD` so `m/_EAD=80` .

We are given `m/_BCA=44 ==>m/_ACD=56` .

AECD is a cyclic quadrilateral (the opposite angles are supplementary.)

Thus the diagonals of AECD form two pairs of similar triangles. (There are a pair of vertical angles, and the other angles intercept congruent arcs.)

Let F be the point of intersection of ` bar(AC)` and `bar(ED)` .

Then `Delta AEF` ~ `Delta DCF` and `/_AED cong /_AEF cong /_DCF cong /_DCA` .` `

----------------------------------------------------------------

`m/_AED=56`

----------------------------------------------------------------

**Sources:**