An easy way to measure the coefficient of static friction is to place two objects together and then tilt them until the top one slides. The angle is directly related to the coefficient.
When the two objects are horizontal there is no frictional force. As the objects are slowly tilted, the force of static friction must increase from zero to counteract the component of the force of gravity that acts along the interface.
Eventually, as the angle increases, that component of the force of gravity exceeds the maximum value of the force of static friction, and the top object slides off.
How does the angle at which this occurs relate to the coefficient of static friction?
Take the limiting case, the angle reached just before the block begins to slide, and draw the free-body diagram.