Thread: geometry

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


thanx

3 diagrams to illustate

Internal angles in a quadrilateral add up to 360

So angle DAB = 160

This is bisected by line to E so

angle DAE = angle BAE = 80

From second diagram angle DAC = 180 - 60 - 56 = 64

angle CAE = angle DAE - angle DAC = 80 - 64 = 16

angle AEC = 180 - 16 - 44 = 120

Thinking of rest

Stuck on rest. Needs either angle ADE or angle DEC or angle BED

If length of AB = length of AD I have an answer

New diagram

Call the point where the lines cross in the centre F

angle ADE = 100 - X

angle DEC = 120 - X

angle CFE = X + 16 = angle AFD

angle CDE = X - 40

angle DFC = 164 - X = angle AFE

If we can find a numerical value for any of these angles we have solved it