Codeando en Angular 9

file.service.ts

import {
  Injectable
} from '@angular/core';
import {
  HttpClient,
  HttpHeaders,
  HttpErrorResponse
} from '@angular/common/http';
import {
  throwError
} from 'rxjs';
import {
  catchError,
} from 'rxjs/operators';
import {
  environment
} from '../../environments/environment';

const httpOptions = {
  headers: new HttpHeaders({
    enctype: 'multipart/form-data'
  })
};

@Injectable({
  providedIn: 'root'
})
export class FileService {
  constructor(
    private http: HttpClient,
  ) {}

  uploadFile(fileUpload: File, id: number) {
    const formData: FormData = new FormData();
    formData.append('File', fileUpload, fileUpload.name);

    return this.http
      .post(environment.baseUrl + `uploadfile/${id}`, formData, httpOptions)
      .pipe(
        catchError(this.handleError)
      );
  }

  private extractData(res: Response) {
    const body = res;
    return body || {};
  }

  private handleError(error: HttpErrorResponse) {
    if (error.error instanceof ErrorEvent) {
      console.error('An error occurred:', error.error.message);
    } else {
      console.error(
        `Backend returned code ${error.status}, ` +
        `body was: ${error.message}`);
    }
    return throwError('Something bad happened; please try again later.');
  }
}

file.component.ts

import {
  Component,
  OnInit,
} from '@angular/core';
import {
  FileService
} from '../../services/file.service';
import {
  FormBuilder,
  FormGroup,
  Validators
} from '@angular/forms';


@Component({
  selector: 'file',
  templateUrl: './file.component.html',
  styleUrls: ['./file.component.css']
})
export class FileComponent implements OnInit {
  validateForm: FormGroup;

  constructor(
    private fileService: FileService,
    private fb: FormBuilder,
  ) {}

  ngOnInit(): void {
    this.validateForm = this.fb.group({
      img1: [null, [Validators.nullValidator]],
      img1Source: [null, [Validators.nullValidator]],
    });
  }

  onFileChange(event) {
    if (event.target.files.length > 0) {
      const file = event.target.files[0];
      this.validateForm.patchValue({
        img1Source: file
      });
    }
  }

  save(fileUp: File) {
    this.fileService.uploadFile(fileUp, id)
      .subscribe(
        (res) => {
            // todo
        },
        (error) => {
          this.toastr.error('Error al insertar datos');
        }
      );
  }
}

file.component.html

<div class="container">
  <div class="row">

    <form [formGroup]="validateForm" (ngSubmit)="save(validateForm.value)" novalidate>

      <div class="form-group row">
        <label for="img1" class="col-3 col-form-label">imágen 1</label>
        <div class="col-9">
          <input type="file" class="form-control-file" formControlName="img1" id="img1" (change)="onFileChange($event)">
        </div>
      </div>

      <button type="submit" class="btn btn-outline-primary">
        Crear <fa-icon [icon]="faPlus"></fa-icon>
      </button>

    </form>

  </div>
</div>

Codeando en C#

FileController.cs

using System;
using System.IO;
using System.Web;
using System.Web.Http;

namespace api.Controllers
{
    [RoutePrefix("api/uploadfile")]
    public class FileController : ApiController
    {
        private routineEntities db = new routineEntities();

        public IHttpActionResult uploadfile()
        {
            var httpRequest = HttpContext.Current.Request;

            if (httpRequest.Files.Count <= 0)
            {
                return Json(500);
            }

            var fileSave = httpRequest.Files[0];
            var filePath = HttpContext.Current.Server.MapPath("~/UploadedFiles/" + fileSave);

            try
            {
                postedFile.SaveAs(filePath);
            }
            catch (Exception ex)
            {
                throw ex;
            }
            return Json(fileSave);
        }

    }
}