Practice (lots of it), with a range finder. Another mental trick is to take a known distance (rugby field length is good) and estimate how many times it fits into what you are seeing.
When I walk the dogs in the hills I take a rangefinder. Estimate the range, and then confirm with range finder.
If you don't have a range finder, use a topo map and baseplate compass with romer scale (100m divider). Try to identify features at the same contour level and measure.
For angle values, a quick rule of thumb is that a closed fist is about 10 degrees. You can confirm this by checking how many times you can fit a closed fist with your arm extended into a 90 degree arc. It is close enough for using when shooting.
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