Hi,

I would say it depends how the plant leaves look like but usually you can determine the angle by applying blob analysis e.g. regionprops and orientation, MajorAxisLength. The stem should usually have a different shape than the leaves (relation between major and minor axis) as well as different texture

Have a look at Hough Lines: http://cn.mathworks.com/help/images/ref/houghlines.html

If you are seeing the leaf and stem separately (not overlapping) and you cannot see the face of the leaf then you are viewing the leaf as a thin line and the angle it makes with the stem is the true angle.

For any other case, if you only have a 2D image (not a depth image) then the true angle in 3D is projected onto a 2D image through a perspective projection. This means that the true angle may not be the same that you might get using any of the aforementioned methods.

This being said, if you're fine with the projected angle, you can segment the leaf using color, texture, kmeans or any of the several methods that exist. Then use skeletonization to approximately find the center line of the leaf and then use hough transform to fit lines to this center line of the leaf and the stem. If you know two points on each line that gives you the equation of the line and you can then find the angle.