Why did austria-hungary annex bosnia and herzegovina? 1.  to create a larger divide between france and russia2. to take advantage of trade routes on the adriatic sea3. to prevent russia from taking ottoman empire territory4. to seize territory from the declining ottoman empire

I believe it’s number 4: to seize territory from the declining Ottoman Empire

Why did Austria-Hungary annex Bosnia and Herzegovina?

The correct answer is:
4. to seize territory from the declining Ottoman Empire

The Bosnian crisis of 1908–09, also known as the Annexation crisis or the First Balkan Crisis, erupted when on 8 October 1908, Austria-Hungaryannounced the annexation of Bosnia and Herzegovina, territories formally within the sovereignty of the Ottoman Empire. This unilateral action—timed to coincide with Bulgaria's declaration of independence (5 October) from the Ottoman Empire—sparked protestations from all the Great Powers and Austria-Hungary's Balkan neighbours, Serbia and Montenegro. In April 1909 the Treaty of Berlin was amended to reflect the fait accompli and bring the crisis to an end. The crisis permanently damaged relations between Austria-Hungary on one hand and Serbia, Italy and the Russian Empire on the other. The Italian historian Luigi Albertini regarded it as laying the grounds for World War I. Although the crisis ended with what appeared to be a total Austro-Hungarian diplomatic victory, Russia became determined not to back down again and hastened its military build-up. Austrian–Serbian relations became permanently stressed.