Detente did not end the Cold War.  The lessening of the nuclear arsenal was a political football passed around by the 3 major nuclear powers at the time, mostly to avert a first strike from which the world narrowly escaped during the early 1960's.  By the latter 1960's until the 1990's, Detente became an important piece of negotiations between powers, but was not the critical factor that ended the Cold War. What brought about the end of the Cold War was not so much regarding a nation's nuclear arsenal, but rather a concerted effort by the United States to economically outstrip the Soviet Union.  Part of that endeavor promoted the rebuilding of Germany and Japan by the US after World War II to establish strong democracies to contain the spread of Communism.

The short answer is that it didn't.  Beginning in the 1970's with Richard Nixon's visit to China and negotiations with the Soviet Union over nuclear arms, all detente did was lessen the tensions between us and the Soviet Union and China, and laid the groundwork for future negotiations. 

What actually ended the Cold War was the Soviet Union's loss of Eastern Europe as its satellite nations and its economic and political collapse in 1991.  As for China, increasingly good trade relations have softened relations between us and them,

I am not really sure that detente did end the Cold War.  Many people would argue that Reagan's more aggressive pursuit of a big military ended the Cold War.  But if I had to argue that detente did it, I would say:

• It put more pressure on the Soviet Union.   With detente, Soviet citizens came to know more about the West.  When they did, they became more and more dissatisfied with how bad their lives were compared to those of westerners.
• Perhaps you can say that better relations with China (part of detente) helped by making the Soviets a bit more isolated.

But if you are really in 10th grade asking this, there is probably a specific answer that your textbook gives.  You should probably try to find it because that's the answer your teacher is going to expect.