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The measurements of chemical abundances in polar-ring galaxies (PRGs) are important to distinguish between different scenarios of their formation. However, up to now the metallicity measurements were made only for few PRGs. We studied the ionization state and oxygen abundance distribution in a sample of PRGs from the long-slit spectroscopic observations carried out with the SCORPIO-2 focal reducer at the Russian 6-m telescope. We show that ionization by young stars dominates in the external parts of polar discs, while shocks have a significant contribution to gas excitation in the inner parts of polar structures. This picture was predicted earlier in a toy model implying the collision between gaseous clouds on polar orbits with the stellar disc gravitational potential well. The exception is a moderately inclined ring to the host galaxy NGC 5014: the accreted gas in the centre has already settled on the main plane and ionized by young stars, while the gas in the internal part of the ring is excited by shocks. The present study three times increases the number of polar structures with an available oxygen abundance estimation. The measured values of the gas metallicity almost do not depend on the galaxy luminosity. The radial [O/H] gradient in the considered polar rings is shallow or absent. No metal-poor gas was detected. We ruled out the scenario of the formation of polar rings due to cold accretion from cosmic filaments for the considered sample of PRGs.