Inspired by the answer https://stackoverflow.com/questions/36265026/angular-2-innerhtml-styling, it worked If I change all of my classes to the format :host >>>  selector i.e. (the commented part was what I was using earlier. I changed from class (eg close-cross-link to selector by giving an id to a (a#close-button)
:host >>>  a#close-button /*.close-cross-link*/ {
  border: 1px solid black;
  width: 100px;
  height: 100px;
  opacity: 0.3;
  background-color:white;
  position:relative;
  top:-15px;
  left:-15px;
  /*border-radius:50%; /*makes a circle*/
}
:host >>>  a#close-button:hover /*.close-cross-link:hover */{
  opacity: 1;
}
:host >>>  a#close-button:before, :host >>>  a#close-button:after /*.close-cross-link:before, .close-cross-link:after*/ {
  display:inline-block;/*need display+relative+left or absolute+left*/
  position:relative;
  left: 13px;
  border: 1px solid black;
  top:0px;
  right:0px;
  content: '';
  height: 31px;
  width: 2px;
  background-color: #333;
  border-radius:50%; /*makes cross sharper*/
}
:host >>>  a#close-button:before /*.close-cross-link:before */{
  transform: rotate(45deg);
}
:host >>>  a#close-button:after /*.close-cross-link:after*/ {
  transform: rotate(-45deg);
}