It´s simple You set the minWidth or minHeight, depends on what you are looking for, horizontal or vertical. And for the other object(the one that you want to fill the remaining space) you set a weight of 1 (set the width to wrap it´s content), So it will fill the rest of area.
<LinearLayout
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_weight="1"
android:gravity="center|left"
android:orientation="vertical" >
</LinearLayout>
<LinearLayout
android:layout_width="80dp"
android:layout_height="fill_parent"
android:minWidth="80dp" >
</LinearLayout>