Need help determining angles inside an irregular hexagon

[sw98]

This might seem like a really dumb question, but I need some help determining some angle measurements.

I am trying to build something that's shaped like an irregular hexagon. I've attached a picture of it below and I've tried my best to draw it to scale. Also, I drew some lines in to break it up into 2 right triangles and an isosceles trapezoid. Some values are known, but I am struggling on determining angles a and f and c and e. Once I can determine any of those, I should be ok with solving the lengths of the sides.

Does anyone know how angles "a" and "f" can be solved or is there not enough information present?

 

[Ishuda]

This might seem like a really dumb question, but I need some help determining some angle measurements.

I am trying to build something that's shaped like an irregular hexagon. I've attached a picture of it below and I've tried my best to draw it to scale. Also, I drew some lines in to break it up into 2 right triangles and an isosceles trapezoid. Some values are known, but I am struggling on determining angles a and f and c and e. Once I can determine any of those, I should be ok with solving the lengths of the sides.

Does anyone know how angles "a" and "f" can be solved or is there not enough information present?

If the 25 is the only measurement you have other than the measure of all the main angles (90, 120, and 150 degrees), you do not have a unique figure. For example you could continue the line ED out another mile, draw the 90 degree angle, go a distance of 25 and make the turn to the equivalent CB. Angle b^o would be much less but then angle h^o would increase to make up for it. Once the point B had reached point E horizontally, you could, at any point pass that, drop a perpendicular and do a mirror of what you had to complete the figure. Thus you can make b^o anything you want from about 0 (point D is very far from point E) to about 90 degrees (point D is very close to point E).

 

[soroban]

Hello, sw98!

I am trying to build something that's shaped like an irregular hexagon.
I've attached a picture of it below and I've tried my best to draw it to scale.
Also, I drew some lines in to break it up into 2 right triangles and an isosceles trapezoid.
Some values are known, but I am struggling on determining angles \(\displaystyle a,f,c\) and \(\displaystyle e.\)
Once I can determine any of those, I should be ok with solving the lengths of the sides.

Does anyone know how angles \(\displaystyle a\) and \(\displaystyle f\) can be solved,
or is there not enough information present?

We need at least one more length.

Take the side \(\displaystyle EF\) and slide it up an inch or two,
\(\displaystyle \quad\)keeping it parallel to side \(\displaystyle BC\).

The six vertex angles are unchanged.
But we see that angle \(\displaystyle a\) is smaller.

There is insufficient data for a unique hexagon.