SolvingSoloist
Since, AB|| CD and AC is transversal angle DCA =angleCAB (alt. int. angles) Similarly, angleCDB =angleDBA (alt. int. angles) In AOB and COD, angleAOB =angleCOD (V.O.A) angleOAB = angleOCD angleOBA = angleODC So, these two triangles are similar (AAA similarity) Þ AO/CO = OB/OD Þ (3x-19)/(x-3) = (x-4)/4 On solving, you get x = 8 or x = 11 That's my answer. Hope it helps.
Answers & Comments
angle DCA =angleCAB (alt. int. angles)
Similarly, angleCDB =angleDBA (alt. int. angles)
In AOB and COD,
angleAOB =angleCOD (V.O.A)
angleOAB = angleOCD
angleOBA = angleODC
So, these two triangles are similar (AAA similarity)
Þ AO/CO = OB/OD
Þ (3x-19)/(x-3) = (x-4)/4
On solving, you get x = 8 or x = 11
That's my answer.
Hope it helps.