How did the boxer rebellion strengthen american ties with china?

the united states supported the rebels and gained their support.
the united states provided troops to fight the rebels.
the united states sent arms and financial support to the chinese government.
the united states thwarted attempts by great britain and germany to fortify the rebels.

During the Boxer Rebellion, the United States provided troops to fight the rebels.

Explanation:

The United States participated in the Eight-Nation Alliance, which was formed to stop the Boxer Rebellion in China.

After the start of the Boxer Rebellion in November 1899, the attack on the businesses and industries of the foreigners living in northern China began, as well as the killings of foreigners and Chinese people converted to Christianity. Foreign diplomatic delegations were also threatened by boxers, supported by some soldiers of the Chinese imperial army.

To this end, on May 31, the foreign military commanders located in the area sent a multinational force of 475 men from the foreign naval troops closest to Beijing, to collaborate in the defense of the fenced-in delegations. It soon became clear that such forces would be insufficient and the idea of a more extensive military intervention gained ground. Before that, the countries that had interests in Chinese territory decided to fight the revolt by themselves, given the inefficiency of the Chinese government and the sympathy that boxers had among various high officials of the administration and the army of the Qing Dynasty.  

The foreign governments in June sent a second force of 2,000 soldiers, mostly British, Russians, and Japanese, from the port of Takou in the Yellow Sea to Tianjin, in order to repel the rebels and make their way to Beijing.

In order to definitively crush the revolt (and not only to rescue the delegations of Beijing) it was determined to form a large multinational force, giving rise to the Alliance itself. The troops of the Alliance were formed by contingents of infantry, cavalry and artillery troops, with the support of marines, as well as warships, belonging to eight different nations and totaling an approximate total of 55,000 men between ground soldiers and naval troops.

The troops sent initially included detachments of powers that had garrisons within Chinese territory, like Great Britain in its concession of the port of Weihai, France in the southern region of Hunan (bordering with the French Indochina) and Germany in the port of Qingdao, or in countries that had territory bordering China (such as Russia and Japan), although afterwards they were reinforced with contingents from their countries of origin. The contingents of Italy and Austria Hungary (states that lacked colonies in Asia) came out of the small concessions that both countries had in China and were exclusively formed by naval troops, while US troops were sent from the Philippines.

Due to the aforementioned reasons, the foreign contingent consisted mostly of Japanese soldiers (20,840 men), together with 13,150 Russians, 12,020 British, 3,520 French, 3,420 Americans, 900 Germans, 80 Italians, and 75 Austro-Hungarians.

i believe it would be capitalism

it increased the power of the king of england.