der Angehöriger
relative
A person who belongs to another person's family; a relative. Often used in the plural (die Angehörigen).
Die Polizei benachrichtigte die Angehörigen des Opfers.
The police notified the victim's relatives.

relative / member
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relative
A person who belongs to another person's family; a relative. Often used in the plural (die Angehörigen).
Die Polizei benachrichtigte die Angehörigen des Opfers.
The police notified the victim's relatives.

'Der Angehörige' is a nominalized participle of the verb 'angehören' (to belong to). So it describes a person who 'angehört' (belongs) to a group or family.
Als Angehöriger dieser Universität haben Sie Zugang zur Bibliothek.
As a member of this university, you have access to the library.
Since this word is a nominalized adjective, it is also declined like an adjective. Pay attention to the endings, e.g. 'ein Angehöriger' (nominative), 'des Angehörigen' (genitive), 'die Angehörigen' (plural).
Die Polizei sprach mit einem Angehörigen der Familie.
The police spoke with a relative of the family.
You can recognize the meaning from the context: If the word appears in the plural ('die Angehörigen') without further specification, it usually means family members. If it appears in the singular with a genitive complement or a 'von' complement, it means a member of an organization.
Die Ärzte informierten die Angehörigen über den Zustand des Patienten.
The doctors informed the relatives about the patient's condition.
In the meaning 'Familienmitglied' (family member), the word is often used in the plural ('die Angehörigen') and in official contexts, for example by hospitals, the police, or in death notices.
Das Krankenhaus bittet die Angehörigen, telefonisch Kontakt aufzunehmen.
The hospital asks the relatives to get in touch by phone.
When 'Angehöriger' describes a member of a group, the group usually follows in the genitive or with the preposition 'von'. The genitive form is more common in written language.
Sie ist Angehörige einer religiösen Minderheit.
She is a member of a religious minority.
family
'die Familie' and 'der Angehörige' both belong to the area of family relationships. 'Familie' refers to the whole group, for example parents and children or all relatives. 'Angehöriger' refers to one individual person from this group; very often, people use the plural 'die Angehörigen'. The words can be confused because both talk about close personal relationships. If you mean the group, use 'Familie'. If you mean an affected person or several individual relatives, 'Angehörige' fits better, for example in a hospital or in official information.

Die Ärztin spricht nach der Operation mit den Angehörigen.
After the operation, the doctor speaks with the relatives.
Meine Familie besucht mich am Wochenende.
My family is visiting me at the weekend.