Reddit mentions of General Tools 822 Digital Angle Finder Rule, 5-Inch

You would have to subtract the outer angle from 180.

Carpenters would have something like this "angle finder", which you could buy or borrow.

If you want to do it quick and dirty, just take two sticks (like paint stirrers maybe) and fasten them together at the end like the professional angle finder linked above. Put them in the spot you need to measure, pinch it tight once you have the angle, then lay it down on a piece of cardboard and mark it out with a pen. Cut the cardboard out and make sure it fits. Then use it as a template to cut your wood.

I have a cheap old Delta 10” miter saw that cuts great 45s with the following setup.

Use a digital angle finder to set the bevel and angle. I don’t trust the built in detents or bevel gauge. It also helps with squaring the fences.

https://www.amazon.com/dp/B00563TM32/ref=cm_sw_r_cp_api_i_s8HvCbWY8TNCC

When cutting smaller pieces, a zero clearance fence really helps get a precise cut. You can align the work piece to the kerf line in the fence to get an exact cut. I replicated the one in this video.

https://youtu.be/UjB1UpNqY2k

I also use a middle of the road Diablo 60 tooth blade in the saw for cleaner cuts. I keep a 40 tooth in the table saw and also have an 80 on hand for really fine work. Both saws are 10” so I can move the blades between them if necessary.

Good luck, I spent a lot of time building scrap frames practicing 45s. Decent corner or band clamps are also a must have for assembly!

Tom Silva did a great segment on Ask This Old House about finding weird angles for kitchen crown molding when the cabinets weren't square. I can't find it for the life of me though, so I'll try to describe it in text. Edit found it! Starts about 13 minutes in.

For outside corners, take two pieces of 1x3 or 1x4, about a foot long. Hold one to each wall with some hanging past the corner, so that they overlap. With the pieces tight against the wall, trace the edge on the piece below/above it, and also mark both pieces on the v between them. Take the pieces and draw a line from the v mark to the end of the line against the corner, and that's the angle you need to cut a perfect miter. Simply line up your saw blade using that as your guide, then cut the molding piece. Use the same process on the other board to get the guide for the other side of the miter. Adapting the same process to inside corners is left as an exercise for the reader, assuming you don't want to cope one side.

Or, use a digital angle finder.

square posts are "traditional" for picket fences but it's easily doable w/ round posts and/or rails. just use google images and you'll see there are infinite variations in design. you can buy pre-drilled fence posts at most big box stores or buy a hole cutter and make your own.

to do mitres for square posts hold your rail up to the post and use an angle finder to find the proper cut.

this is intro to carpentry stuff. is this your first diy project?

Definitely go with the pine over the MDF. That stuff is just junk. Mitering baseboard can be a pain because your walls are seldom ever square. You need to learn how to cope the corners in if you want to have the best looking job. That said, you can indeed use the squared stock with butt joints. Just be aware that if the corners are not square you may still get some gaping. I'd invest in a digital angle finder gauge. https://smile.amazon.com/General-Tools-822-Digital-Finder/dp/B00563TM32/ref=sr_1_5?ie=UTF8&qid=1504089848&sr=8-5&keywords=angle+finder to get an accurate measurement of the inside angle. Then you can get a better miter or butt joint. The problem with the square stock is that it's a dust collector since it's just a flat top. You can stack a molding on top of it later though if you decided it just isn't working to make it look more like a traditional baseboard. Squared trim will be a more modern or contemporary look compared to the colonial style trim to linked to.

I think there's a really high chance that your miter saw isn't doing the angle you think it is, which is just a function of tools not being perfect. It could also be that your window trim isn't dead on 45 degrees. I would recommend trying something like this:

https://www.amazon.com/General-Tools-822-Digital-Finder/dp/B00563TM32

Set your miter saw to the angle based on an external tool, not the fence (unless you know for a fact your fence is dead nuts accurate). I had a huge problem doing this with some trim work until I started using an external guide instead of assuming the fence was right.

Are there any particular measuring tools you recommend, aside from a good set of calipers, a solid ruler, and a gap gauge?

I'm thinking about grabbing this to help with figuring out angles on objects.