you have to use a resource dictionary. something as below.
<UserControl.Resources>
<ResourceDictionary>
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="../Resources/Styles.xaml"></ResourceDictionary>
</ResourceDictionary.MergedDictionaries>
<vm:UpdateControlViewModel x:Key="UpdateControlViewModel"></vm:UpdateControlViewModel>
</ResourceDictionary>
</UserControl.Resources>
considering your styles.xaml page is in resources folder of your project. hope this helps.