Limit rotation of z axis of a 2d object which rotates with mouse click and drag

@theleonn just add a check for value of (angle + angleOffset) before applying the rotation.

 using UnityEngine;
  using System.Collections;
  
  public class ButtonController3 : MonoBehaviour {
  
      private Camera myCam;
      private Vector3 screenPos;
      private float angleOffset;
  
  
      void Start () {
          myCam = Camera.main;
      }
  
      void Update () {
          //This fires only on the frame the button is clicked
          if (Input.GetMouseButtonDown (0)) {
              screenPos = myCam.WorldToScreenPoint (transform.position);
              Vector3 v3 = Input.mousePosition - screenPos;
              angleOffset = (Mathf.Atan2 (transform.right.y, transform.right.x) - Mathf.Atan2 (v3.y, v3.x)) * Mathf.Rad2Deg;
          }
  
          //This fires while the button is pressed down
          if (Input.GetMouseButton (0)) {
              Vector3 v3 = Input.mousePosition - screenPos;
              float angle = Mathf.Atan2 (v3.y, v3.x) * Mathf.Rad2Deg;
 
 
    float newAngle = angle + angleOffset;
 
             
             if (newAngle < 0f && newAngle > -160f)
             {
 
                   transform.eulerAngles = new Vector3(0, 0, angle + angleOffset);
 
             }
          }
      }
  }