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S-character basically refers to what fraction of the hybridized orbital is made up from the s-orbital. For example, sp has greater s-character than sp^2. Because there are fewer sp hybridized orbitals than there are sp^2 hybridized orbitals, 2 versus 3, as the s-character increases and the number of orbitals decrease, the orbitals are located farther apart from each other. Therefore, the bond angles increase.
The s character basically means the percentage of sigma bond in a hybridization. In a linear lewis structure there is a hybridization of sp. This has an s character of 50% and a p character of 50%. The bond angle is 180. Now if we look at a trigonal planar lewis structure, there is a decreased bond angle of 120 and a new hybridization of sp2. The percentage of the sigma bond decreases to 33%. Since s character and bond angles are directly proportional, as one increases, so does the other.
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