Final answer:
Portugal was recognized as an independent country in 1143 and became a republic in 1910 after a revolution.
Step-by-step explanation:
The Iberian country that was recognized in 1143 and became a republic in 1910 is Portugal.
In 1143, the Treaty of Zamora was signed, which recognized Portugal's independence from the Kingdom of León.
Then, in 1910, Portugal transitioned from a constitutional monarchy to a republic after the revolution that overthrew King Manuel II.