This photo from the 1930s shows us Wilshire Blvd as it angles to the left at Lafayette Park. I’ve just recently learned why all those downtown streets hit Hoover Street and then make a turn. When Los Angeles was originally laid, the founders followed the Spanish way of laying a street grid—orienting 45 degrees off the cardinal directions. By the time LA’s spread reached where Hoover Street now, the city adopted the American way of laying out streets, which is to orient them along the north-south and east-west points of the compass.

UPDATE: from Peter Heffner:

This is an urban myth.

Ord made the first survey and laid out the first grid in 1849. The Spanish did no survey and did not lay out any grid.

The change in angle is because of the edge of the Spanish one-league square land grant. However, there is no Spanish grid. All grids were laid out by American surveyors according to American rules.

The reason the angle changes at the edge of the land-grant is because that was the city limits when they surveyed the city. When more land was annexed, it was surveyed, too, and the expansion was laid out to true north.

The reason for the odd angle inside the old city limits is because Ord aligned Main Street to the edge of the bluff up from the river, to keep the city above flooding. Then, he aligned the grid to Main Street.