So here's some explanation of each step.

To make the base shape I drew 2 circles and a rectangle between them and used Construct > Boolean > Union to combine them, then did the same for the oblong opening and then drew a circle at the other end, then selected them and ran Construct > Extrude to make the base part.

Then I drew in an angled line for the desired angled bend axis, I moved it to the top surface by dragging it in a side view.

I then selected the bend axis and ran Construct > Offset with the "Both sides" option enabled to make 2 cutting lines on either side of the bend axis. Then select the part and run Edit > Trim, and select the 2 offset lines as the cutting objects. Select the inside piece as the piece to discard and then right-click to finish Trim, now the piece is cut into 2 separate objects.

Select the piece you want to rotate and then rotate it by your desired angle around the pivot axis by running Transform > Rotate > Rotate axis, snap the rotation axis points onto the ends of the center pivot line.

Now to get a good quality connecting surface that does not buckle or warp too much is a little tricky. I think it's probably best to make a extruded shape that has its extrusion direction going in the pivot axis direction and then trim that down afterwards.

To make the profile to extrude I put in 2 lines and then used Construct > Blend to make a smooth blend curve connecting them. Then the blend curve is what you extrude.

To position the lines correctly I started by drawing in one line like this, first point snapped on to the midpoint, and second one along the "Perp" snap, looks like this:



Then the trick is to get the line on the other side positioned in the aligned spot. To do that start drawing a second line but before you place the first point you will drag out a construction line to make a snap point at the correct location.

The way that looks is, after you have started the line command, move your mouse over the start point of the line you just previously drew, here:



Now click and hold down the mouse button and while keeping it held down drag out a construction line, while still holding the mouse down move over to the other edge and find the "perp" snap over there, release the mouse button when you find it, looks like this:



Now that construction line has ended where you want to start the line at, there will be an "end" snap there now so click it for the start point of your line, and then place the second point at a "perp" straight snap spot same as the other line, looks like this:




Now select the 2 lines near their ends you want to connect and run Construct > Blend to build a blend curve which looks like this:




Repeat that on the underside as well. Then select the blend curves, run Construct > Extrude and check the "Both sides" option and build the extended bridging surfaces.

After that switch to the Top view and draw in some cutting lines between endpoints, and then select the extended extrusions and run Edit > Trim, and use the cutting lines to cut off the ends.

Then the remaining areas can be surfaced by selecting the 4 boundary edges and running Construct > Network. After that select all the pieces and use Edit > Join to glue them together into a finished solid.


Hope this helps!

- Michael