Joints for a 3/4in-thick pentagon

Question

I'm attempting to create a pentagon from 3/4in-thick pine boards, which will become part of a slightly odd shelving unit. Of the five angles, two are 90 degrees and I'm planning to use dowels and glue to connect them. The remaining angles are between 110 and 140 degrees, and I'm looking for some advice how to best join them.

Just glue? At those angles, I'm not sure the dowels will do much.

Also, any suggestions how to fixate the parts while the glue is solidifying?

Update per request: Here's a rough drawing. The plan is to add the middle board after the rest is complete. (And before you ask, the contraption is going to be 1) installed in a nook, 2) screwed to the wall on the left, 3) have a similar, smaller sibling, but flipped horizontally, 4) the sibling will rests on top of the upper-right board with a parallel board on its own, and 5) the sibling will be screwed to the right wall of the nook.)

Answer 1

I'm looking for some advice how to best join them.

This will depend mostly on how much load you expect to put on the shelf and how you are mounting the shelf to the wall (if this is a freestanding shelf, don't worry about the mounting part).

The simplest means would be to to a regular blued butt joint at your angles. This is as easy as it sounds - just glue the two faces, press, and wait.

The second would be to spline the angle. There are two ways to do this: one with the spline parallel to the width of the joint

(source: LumberJocks)

and the other with the splines (also called "keys") across the joint

(source: another WW Question)

At those angles, I'm not sure the dowels will do much.

You are correct. Not only will the dowels not do much at weird angles, forming the joint will be an exercise in confusion and frustration.

Also, any suggestions how to fixate the parts while the glue is solidifying?

One simple way to glue weird miters is to wrap the outside of the piece in masking tape and just "roll it up."

(source: WorkshopDemos.com)

Otherwise, one could also glue sacrificial clamping blocks to the outer faces such that the faces of the clamping blocks are parallel. Then, the clamps have a straight path to clamp to and will bring the pieces together more easily.

(source: Woodworking.com)

Answer 2

My biscuit joiner is able to cut slots at angles which could work for this. Also, depending on the size, the glue might be more than enough to keep everything together.

As far as keeping it all together, I've used ratchet straps/tie downs to hold odd-shaped things together for gluing. My sister had a (purposely) odd-shaped dresser with no place for a clamp to hold the broken piece at the correct angle. The ratchet strap not only was able to hold it at the right angle, it didn't mar the wood either!

Answer 3

Just glue? At those angles, I'm not sure the dowels will do much.

If I'm imagining the construction properly these would still be end grain to end grain joints, which is the weakest glue-only joint. In the right circumstances that can actually be strong enough, but ideally it should be reinforced in some way.

So dowels would do a lot here if you wanted to go that way.

Also, any suggestions how to fixate the parts while the glue is solidifying?

I'm a big fan of the tape method already suggested by grfrazee, when done right it works really well. Another demo of it here on Popular Woodworking, with video and stills images.