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Most muscles work in pairs, and when a muscle works it needs to have an agonist and an antagonist, unless the muscle's natural state is opposite to that which is produced by the muscle, example Sphincter ani externus muscle.
Antagonistic pairs are located in opposite sides of a joint or bone.
An "antagonist" is a classification used to describe a muscle that acts in opposition to the specific movement generated by the agonist and is responsible for returning a limb to its initial position.
Antagonistic pairs 
Antagonistic muscles are found in pairs called antagonistic pairs. As one muscles contracts, the other relaxes. For example the biceps contracts and the triceps relaxes.
These consist of an extensor muscle, which "opens" the joint (i.e., increasing the angle between the two bones) and a flexor muscle, which does the opposite to an extensor muscle. They include muscles such as triceps and hamstrings, quadriceps and biceps etc.
Antagonistic pairs are needed in the body because muscles can only exert a pulling force, and cannot push themselves back into their original positions. An example of this kind of muscle pairing is the biceps brachii and triceps brachii.
When the biceps are contracting, the triceps are relaxed, and stretches back to its original position. The opposite happens when the triceps contract. Another example on antagonistic pairs; abductor and adductor muscles.