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In the C-C single bonds in cycloalkanes and cycloalkenes, the carbons are all sp3 hybridized. This means that all the carbons want to be 109.5 degrees away from each other. In cyclooctene, all the C-C single bonds are not 109.5 degrees, because if they were, the ends of the ring would overlap instead of meeting. In order to form the ring structure, the angles between carbons must be increased in order to fit all 8 carbons in the ring. Since the angles are greater than 109.5, they wish to return to that state, resulting in ring strain. Think of this as the opposite of cyclopropane and cyclobutane. For those two the angles are too small, while for cyclooctane, the angles are too big.
The most stable ring structure in biology is the cyclohexane and specifically the chair conformation of cyclohexane. Compared to cyclooctene, cyclohexane has less bond angle strain because a ring structure with 8 carbon atoms forces the bond angles of the ring to go way beyond the preferred 109.5 degree bond angle. This means cyclooctene will have more bond angle strain than cyclohexane and thus, more ring strain.
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