sudo: node : command not found

No, sudo does not preserve your $PATH environment variable for security reasons. Instead, it gets replaced with a secure_path defined in /etc/sudoers, which you should not change.

$ sudo grep secure_path /etc/sudoers
Defaults    secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/snap/bin"

You think to have verified that the $PATH variable stays the same with your command

sudo echo $PATH

but actually Bash expands variables before starting to execute any (here the sudo) command, which means the line above shows your own $PATH value. To get the one as sudo, use e.g.

sudo bash -c 'echo $PATH'

What you can do is to e.g. resolve the command you want to run (node or npm) in your own user's shell using process substitution with which:

sudo "$(which npm)" install -g angular-cli
sudo "$(which node)" app.js

This first runs which npm or which node as your user, which returns the absolute path of the executables belonging to the specified commands. Then that output is literally inserted into your sudo command, so sudo actually believes it got executed with absolute paths like below, removing the need to look anything up in $PATH:

sudo /home/dc/node/bin/npm install -g angular-cli
sudo /home/dc/node/bin/node app.js

You could just create a soft link for node, npm and npx in the /sbin directory e.g.

ln -s /usr/local/lib/nodejs/node-v12.14.1-linux-x64/bin/node /sbin/node

Syntax > ln -s (source) (destination)

Now running sudo node should work