Key question is how wide is your frontage (front boundary)?
If you read this section of URA residential handbook (
Setbacks for existing irregular or odd-shaped plots (excluding newly created plots)), there's an example for odd shaped plots like yours.
https://www.ura.gov.sg/Corporate/Gu.../Residential/Terrace/Setbacks-from-boundaries
if your front boundary is more than 8m wide, then you are allowed to do what you had planned as the front setback of 7.5m will need to be applied for 8m from the boundary line joining your neighbour which in this case, starts from the left side.
So assuming you have a frontage of 12m, then what you can built a structure within the 8m to 12m portion of the land. However, the side and front setback of 2m will need to be adhered to as well.
So basically a design like below. The awning/eave from this new structure can extend up to 1m from the building. Note that this 1m reference is from the building where the awning is attached to and not from the boundary line.
So back to the key question of how wide is your plot's frontage and what is the slanted side? if your slanted side boundary falls within 10m when measured at the 7.5m set back line, then you can forget about your plans already. I think in order to build any decent sized room, you will need at least 12m width at that 7.5m setback line which means your frontage would actually be much much wider than 12m. You can PM me directly with your plot details if you want.