The behavior you’re describing is know as “polar mode”. (The term is from CAD.). You can turn polar mode on or off by clicking the button in the measurement toolbar.
When adding points in polar mode, the point is forced to fall on a line that is a multiple of 90 degrees from the previous point. This is most commonly used to create horizontal or vertical lines. It can also work for lines of various angles. Select the desired angles by checking the appropriate box(es) on the Admin/User Preferences/Drawing tab. You can also disable polar mode when creating measurements with a Count data type on the Drawing tab of the User Preferences Window