Change the color of a checked menu item in a navigation drawer

Well you can achieve this using Color State Resource. If you notice inside your NavigationView you're using

app:itemIconTint="@color/black"
app:itemTextColor="@color/primary_text"

Here instead of using @color/black or @color/primary_test, use a Color State List Resource. For that, first create a new xml (e.g drawer_item.xml) inside color directory (which should be inside res directory.) If you don't have a directory named color already, create one.

Now inside drawer_item.xml do something like this

<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
    <item android:color="checked state color" android:state_checked="true" />
    <item android:color="your default color" />
</selector>

Final step would be to change your NavigationView

<android.support.design.widget.NavigationView
    android:id="@+id/activity_main_navigationview"
    android:layout_width="wrap_content"
    android:layout_height="match_parent"
    android:layout_gravity="start"
    app:headerLayout="@layout/drawer_header"
    app:itemIconTint="@color/drawer_item"  // notice here
    app:itemTextColor="@color/drawer_item" // and here
    app:itemBackground="@android:color/transparent"// and here for setting the background color to tranparent
    app:menu="@menu/menu_drawer">

Like this you can use separate Color State List Resources for IconTint, ItemTextColor, ItemBackground.

Now when you set an item as checked (either in xml or programmatically), the particular item will have different color than the unchecked ones.

I believe app:itemBackground expects a drawable. So follow the steps below :

Make a drawable file highlight_color.xml with following contents :

<shape xmlns:android="http://schemas.android.com/apk/res/android" android:shape="rectangle">
     <solid android:color="YOUR HIGHLIGHT COLOR"/>
</shape>

Make another drawable file nav_item_drawable.xml with following contents:

<selector xmlns:android="http://schemas.android.com/apk/res/android">
        <item android:drawable="@drawable/highlight_color" android:state_checked="true"/>
</selector>

Finally add app:itemBackground tag in the NavView :

<android.support.design.widget.NavigationView
android:id="@+id/activity_main_navigationview"
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_gravity="start"
app:headerLayout="@layout/drawer_header"
app:itemIconTint="@color/black"
app:itemTextColor="@color/primary_text"
app:itemBackground="@drawable/nav_item_drawable"
app:menu="@menu/menu_drawer">

here the highlight_color.xml file defines a solid color drawable for the background. Later this color drawable is assigned to nav_item_drawable.xml selector.

This worked for me. Hopefully this will help.

********************************************** UPDATED **********************************************

Though the above mentioned answer gives you fine control over some properties, but the way I am about to describe feels more SOLID and is a bit COOLER.

So what you can do is, you can define a ThemeOverlay in the styles.xml for the NavigationView like this :

    <style name="ThemeOverlay.AppCompat.navTheme">

        <!-- Color of text and icon when SELECTED -->
        <item name="colorPrimary">@color/color_of_your_choice</item> 

        <!-- Background color when SELECTED -->
        <item name="colorControlHighlight">@color/color_of_your_choice</item> 

    </style>

now apply this ThemeOverlay to app:theme attribute of NavigationView, like this:

<android.support.design.widget.NavigationView
android:id="@+id/activity_main_navigationview"
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_gravity="start"
app:theme="@style/ThemeOverlay.AppCompat.navTheme"
app:headerLayout="@layout/drawer_header"
app:menu="@menu/menu_drawer">

I hope this will help.