I had the same issue when I was making a drop-down menu and a confirmation dialog I wanted to dismiss them when clicking outside.
My final implementation works perfectly but requires some css3 animations and styling. 
NOTE: i have not tested the below code, there may be some syntax problems that need to be ironed out, also the obvious adjustments for your own project!
What i did:
I made a separate fixed div with height 100%, width 100% and transform:scale(0), this is essentially the background, you can style it with background-color: rgba(0, 0, 0, 0.466); to make obvious the menu is open and the background is click-to-close.
The menu gets a z-index higher than everything else, then the background div gets a z-index lower than the menu but also higher than everything else. Then the background has a click event that close the drop-down.
Here it is with your html code.
<div class="dropdownbackground" [ngClass]="{showbackground: qtydropdownOpened}" (click)="qtydropdownOpened = !qtydropdownOpened"><div>
<div class="zindex" [class.open]="qtydropdownOpened">
  <button (click)="qtydropdownOpened = !qtydropdownOpened" type="button" 
         data-toggle="dropdown" aria-haspopup="true" [attr.aria-expanded]="qtydropdownOpened ? 'true': 'false' ">
   {{selectedqty}}<span class="caret margin-left-1x "></span>
 </button>
  <div class="dropdown-wrp dropdown-menu">
  <ul class="default-dropdown">
      <li *ngFor="let quantity of quantities">
       <a (click)="qtydropdownOpened = !qtydropdownOpened;setQuantity(quantity)">{{quantity  }}</a>
       </li>
   </ul>
  </div>
 </div>
Here is the css3 which needs some simple animations.
/* make sure the menu/drop-down is in front of the background */
.zindex{
    z-index: 3;
}
/* make background fill the whole page but sit behind the drop-down, then
scale it to 0 so its essentially gone from the page */
.dropdownbackground{
    width: 100%;
    height: 100%;
    position: fixed;
    z-index: 2;
    transform: scale(0);
    opacity: 0;
    background-color: rgba(0, 0, 0, 0.466);
}
/* this is the class we add in the template when the drop down is opened
it has the animation rules set these how you like */
.showbackground{
    animation: showBackGround 0.4s 1 forwards; 
}
/* this animates the background to fill the page
if you don't want any thing visual you could use a transition instead */
@keyframes showBackGround {
    1%{
        transform: scale(1);
        opacity: 0;
    }
    100% {
        transform: scale(1);
        opacity: 1;
    }
}
If you aren't after anything visual you can just use a transition like this
.dropdownbackground{
    width: 100%;
    height: 100%;
    position: fixed;
    z-index: 2;
    transform: scale(0);
    opacity: 0;
    transition all 0.1s;
}
.dropdownbackground.showbackground{
     transform: scale(1);
}