rightly
US /ˈraɪt.li/
UK /ˈraɪt.li/

1.
in a correct or appropriate way
:
•
She rightly pointed out the error in the report.
•
The decision was rightly criticized by the public.
2.
with good reason; justifiably
:
•
He was rightly proud of his achievements.
•
The public was rightly concerned about the new policy.