When placing a dimension, moving the mouse cursor will cause it to switch between creating a Horizontal, Vertical, or Aligned dimension. However, because your angle is so small, it may be difficult to hit that sweet spot to click and get an aligned dimension.
Instead, after you have selected the geometry but before you click to place the dimension, right-click. In the flyout menu for "Dimension Type", you can select Horizontal, Vertical, or Aligned (in this case, Aligned). This will force it to the type you want, regardless of exactly where you click. It is not possible to change this after placement of the dimension.
Also, note that the geometry you select is important as well. If you select the top or bottom lines, you won't get the necessary flyout options, because it is implied that the dimension would need to be perpendicular to the line you selected. You need to either select two end points, or select the almost-vertical line, to get the right options to fix your issue.
