To pass a value down to a component within Angular's router-outlet, you can use route parameters.

1. In your app-routing.module.ts file, define a parameter in your route by adding a colon in front of the parameter name. For example:

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const routes: Routes = [
  { path: 'product/:id', component: ProductDetailComponent },
];

1. In your component's TypeScript file (in this case, ProductDetailComponent), import and subscribe to ActivatedRoute. You can then access the value of the parameter using the params observable. For example:

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import { ActivatedRoute } from '@angular/router';

export class ProductDetailComponent implements OnInit {
  productId: string;

  constructor(private route: ActivatedRoute) { }

  ngOnInit() {
    this.route.params.subscribe(params => {
      this.productId = params['id'];
    });
  }
}

1. Finally, in the HTML template for the parent component containing the router-outlet, you can pass the value down to the routed component using property binding. For example:

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<!-- app.component.html -->
<router-outlet></router-outlet>

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<!-- product-detail.component.html -->
<h2>Product Detail:</h2>
<p>{{ productId }}</p>

Now, when you visit a URL with the pattern /product/123, the ProductDetailComponent will display "Product Detail:" followed by "123".

To change the :host colors with a button click in Angular, you can use Angular's Renderer2 to set the style of the component's host element when the button is clicked. Here's an example code snippet in TypeScript:

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import { Component, Renderer2, ElementRef } from '@angular/core';

@Component({...})
export class MyComponent {
  constructor(private renderer: Renderer2, private elRef: ElementRef) {}

  changeColors() {
    const hostElement = this.elRef.nativeElement;
    this.renderer.setStyle(hostElement, 'background-color', 'red');
    this.renderer.setStyle(hostElement, 'color', 'white');
  }
}

In this example, we're using the Renderer2 service and the ElementRef to get a reference to the component's host element. When the changeColors() method is called (which could be triggered by a button click), we use the setStyle() method to update the background color and text color of the host element.

Here's a link to the Angular documentation on Renderer2: https://angular.io/api/core/Renderer2

To change the :host properties in parent component's CSS from button click in child component, you need to use @Input and @Output decorators to communicate between the parent and child components.

First, create an @Input property in the parent component that will receive the value from the child component. In the parent component's CSS, use the :host selector to define the style rules you want to change.

Next, in the child component, create an @Output event that will emit the value to the parent component when the button is clicked. In the child component's HTML, bind the button to the event emitter and pass the value as an argument.

Finally, in the parent component's HTML, pass the :host property value to the child component as an @Input binding.

Here's an example code snippet using Angular:

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<!-- parent.component.html -->
<div class="parent" [style.color]="hostColor">
  <app-child (hostColorChange)="onHostColorChange($event)"></app-child>
</div>

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// parent.component.ts
import { Component } from '@angular/core';

@Component({
  selector: 'app-parent',
  templateUrl: './parent.component.html',
  styleUrls: ['./parent.component.css']
})
export class ParentComponent {
  hostColor = '';

  onHostColorChange(color: string): void {
    this.hostColor = color;
  }
}

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<!-- child.component.html -->
<button (click)="changeHostColor('red')">Red</button>
<button (click)="changeHostColor('blue')">Blue</button>

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// child.component.ts
import { Component, Output, EventEmitter } from '@angular/core';

@Component({
  selector: 'app-child',
  templateUrl: './child.component.html',
  styleUrls: ['./child.component.css']
})
export class ChildComponent {
  @Output() hostColorChange = new EventEmitter<string>();

  changeHostColor(color: string): void {
    this.hostColorChange.emit(color);
  }
}

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/* parent.component.css */
:host {
  background-color: lightgray;
  padding: 10px;
}

In this example, the parent component has a :host selector that sets the background color and padding. The child component has two buttons that emit the color strings 'red' or 'blue'. When a button is clicked, the changeHostColor() method in the child component emits the color string to the parent component using the hostColorChange event. The parent component listens to this event and sets hostColor to the emitted value. Finally, the parent component binds hostColor to the :host selector using the [style.color] property binding. The background color and padding will change based on the button clicked in the child component.

To change the :host CSS in a parent component with a button click in a child component, you can make use of Angular's @Input and @Output decorators.

In the parent component, create a variable that stores the CSS for the :host selector. Then, create an @Input decorator that binds this variable to the child component.

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// parent.component.ts

@Component({
  selector: 'app-parent',
  template: `
    <div class="parent-host" [ngStyle]="parentHostStyles">
      <app-child (onButtonClick)="updateParentHostStyles()"></app-child>
    </div>
  `
})
export class ParentComponent {
  parentHostStyles = { 'background-color': 'blue' };

  @Input() 
  set parentHost(css: object) {
    this.parentHostStyles = css;
  }

  updateParentHostStyles() {
    const newStyles = {'background-color': 'red'};
    this.parentHostStyles = {...this.parentHostStyles, ...newStyles};
  }
}

In the child component, create a button that emits an event with the new CSS object. Use the @Output decorator to emit this event to the parent component.

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// child.component.ts

@Component({
  selector: 'app-child',
  template: `
    <button (click)="updateHostStyles()">Change Host Styles</button>
  `
})
export class ChildComponent {
  @Output() onButtonClick = new EventEmitter<object>();

  updateHostStyles() {
    const newStyles = {'background-color': 'green'};
    this.onButtonClick.emit(newStyles);
  }
}

In the example above, the parent component listens to the onButtonClick event emitted by the child component when the button is clicked. This event contains a new CSS object, which is merged with the existing parentHostStyles using the spread operator. This updates the :host CSS for the parent component.

Note that this solution assumes that the parent and child components are in a parent-child relationship. If they are not, you may need to use a service to communicate between them.

Angular is an open-source web application framework based on Typescript that is used to build and maintain dynamic web applications. It is the most popular front-end development framework among developers and is developed and maintained by Google. Angular follows the MVC (Model-View-Controller) architecture.

Code example:

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//importing Angular
import { NgModule } from '@angular/core';

//decorator
@NgModule({

})

Angular is an open-source web development framework used for building user interfaces and single-page applications. It is written in TypeScript and based on the component-based architecture developed by Google. Angular components are a subset of Directives and are used to extend the HTML attributes by adding the component-specific behavior to them.