really difficult geometry: In quad. ABCD, angle ABC = 40°,

[owenthakkar]

really difficult geometry: In quad. ABCD, angle ABC = 40°,

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

Any help would be fantastic. Thank you!

 

[Denis]

Re: **^~~~reeli difficult geometry~~~^**plz help

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

Owen, that is not very difficult...but lengthy!

Here's a few hints (I'll use > to represent angle):
since >BCD = 100 and >BCA = 44, then >ACD = 56
>BAD = 360-40-100-60 = 160; since AE bisects >BAD, then >DAE = 80;
also, from triangle ABE, >AEB = 180-80-40 = 60; so >AEC = 180-60 = 120;
from triangle AEC, >CAE = 180-120-44 = 16, so >CAD = 80-16 = 64

Let AD = 1 (that's my way of doing it!)
You can now calculate lengths of CD, AC, AE, CE using Law of Sines:
as example, 1 / sin(56) = CD / sin(64); CD = sin(64) / sin(56)

You'll need Law of Cosines when you get to calculating length of DE.
Then >AED will be easily calculated: result will be an integer:
(but I'm not giving it to you...it's YOUR homework!)

If you can't follow above, well too bad, so sad :shock:

 

[jacket81]

Okay, let f be the point where AC and ED intersect.
SO, you know <efc + <cfd = 180 degrees, right?

Use that, plus what you come up with other angels to get angle aed.
If you need anymore help, ill tell what i got for that angle (if i'm right).

 

[Denis]

Re: really difficult geometry: In quad. ABCD, angle ABC = 40

C'mon jacket...

1st step:
given is: >ABC = 40, >BCD = 100, >CDA = 60 ;
so >BAD = 360 - 40 - 100 - 60 = 160

2nd step:
given is: E is a point BC such that AE bisects the angle BAD ;
so >BAE = 80 and >DAE = 80 and >AEB = 180 - 80 - 40 = 60, so >AEC = 120

3rd step:
given is: >BCA = 44 ;
so >DCA = 100 - 44 = 56, >CAD = 180 - 60 - 56 = 64, >CAE = 80 - 64 = 16

That gives you all the existing angles;
now draw DE and calculate >AED