[angular] ERROR in The Angular Compiler requires TypeScript >=3.1.1 and <3.2.0 but 3.2.1 was found instead

I also faced similar issues when tried to do ng serve. I was able to resolve it as below.
Note:

C:\Windows\system32> is on windows command prompt
C:\apps\workspace\testProj>  is on VS code Terminal (can also be doable in another command prompt)

Following are the steps which I used to resolve this.

Step1. Verify the cli version installed on command prompt (will be Angular CLI global version)

C:\Windows\system32>ng --version

Angular CLI: 8.3.13

If cli was installed earlier, it shows the global cli version.

If cli was not installed, we may get the error
ng is not recognized as an internal or external command

a. (Optional Step) Install Angular CLI global version

C:\Windows\system32>npm install -g @angular/cli
C:\Windows\system32>npm install -g @angular-cli/latest

b. Check version again

C:\Windows\system32>ng --version
Angular CLI: 8.3.13

Step2. Verify the local cli version installed on your angular project(VS code ide or command prompt cd'd to your project project)

C:\apps\workspace\testProj>ng --version
Angular CLI: 7.3.8

Note: Clearly versions are not in sync. Do the following in your angular project

C:\apps\workspace\testProj>ng update @angular/cli        -> important to sync with global cli version

Note: If upgrade donot work using above command (ref: How to upgrade Angular CLI to the latest version) On command prompt, uninstall global angular cli, clean the cache and reinstall the cli

C:\Windows\system32>npm uninstall -g angular-cli
C:\Windows\system32>npm cache clean or npm cache verify #(if npm > 5)
C:\Windows\system32>npm install -g @angular/cli@latest

Now update your local project version, because cli version of your local project is having higher priority than global one when you try to execute your project.

C:\apps\workspace\testProj>rm -rf node_modules
C:\apps\workspace\testProj>npm uninstall --save-dev angular-cli
C:\apps\workspace\testProj>npm install --save-dev @angular/cli@latest
C:\apps\workspace\testProj>npm install
C:\apps\workspace\testProj>ng update @angular/cli

Step3. Verify if local project cli version now in sync with global one

C:\Windows\system32>ng --version
Angular CLI: 8.3.13

C:\apps\workspace\testProj>ng --version
Angular CLI: 8.3.13

Step4.. Revalidate on the project

C:\apps\workspace\testProj>ng serve

Should work now

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