deservedly
/dɪˈzɜːvɪdli/ adverb C2- In a way or to a degree that is deserved or merited.
From the library
I need not explain myself farther; and though _we_ know this anxiety to be quite needless, yet if she feels it, it will easily account for her behaviour to me; and so deservedly dear as he is to his sister, whatever anxiety she may feel on his behalf is natural and amiable.
Oh, if her voice were only equal to her beauty, she would deservedly be considered the Queen of Birds!” This he said deceitfully; but the Crow, anxious to refute the reflection cast upon her voice, set up a loud caw and dropped the flesh.
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