"अगला दिन सोमवार है ।"
Translation:The next day is Monday.
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अगला is the masculine singular form and अगले is the masculine plural form. (The feminine form is अगली)
अगला दिन सोमवार है - The next day is Monday - अगला is used because दिन here is singular
अगले कुछ दिन ठंडे होंगे - The next few days will be cold - अगले is used because कुछ दिन here is plural
In addition, अगले is also the oblique-case form of अगला to be used when it is the object of a postposition.
Eg: अगले महीने में बारिश होगी - It will rain in the next month - महीना is singular here but because अगला महीना is the object of the postposition में, it is used in the oblique-case form अगले महीने.
It just seems like a bad sentence. I can think of few circumstances in which I would ever say this and not just use "tomorrow" as an adequate synonym. Say the next something else is Monday - the next test, the next holiday, the next trip - but next day is just confusing.
You don't need a ghost postposition here. That only happens when you're dealing with intransitive verbs like आना and जाना which cannot have direct objects (which means a postposition is required) but the postposition is still dropped.
In this sentence, you need to use the oblique case form अगले दिन only if you actually use the postposition.
अगला दिन सोमवार है - 'The next day is Monday' and
अगले दिन को सोमवार है - 'On the next day is Monday'
are both valid sentences.