Protractors are mathematical drawing instruments used to draw and to measure angles. Children typically encounter them in elementary or middle school, when they are learning to produce reasonably accurate geometrical figures in order to explore mathematical relationships between those figures.
Quadrant
A quadrant is an instrument used to measure angles up to 90 degrees; and several versions are employed to calculate readings such as longitude, latitude, and time of day. Quadrants were first used in ancient India to observe solar eclipses, and also during medieval times by Muslim astronomers. From around 1270 the (smaller sized) quadrant was used to solve simple surveying problems, plus for astronomical purposes. Large frame quadrants were used for astronomical measurements, notably determining the altitude of celestial objects. They could be permanent observatory installations, such as mural quadrants around 5–10 metres in height.
A geometric quadrant works in the following manner. Along one edge there are two sights forming an alidade, a device that allows one to sight a distant object and use the line of sight to perform a task. To measure the altitude of a star, the observer views the star through the sights and holds the quadrant so that the plane of the instrument is vertical. A plumb bob hangs to establish the vertical dimension, whilst the line indicates the reading on the arc’s graduations.
Smaller quadrants were portable. However, the accuracy of the instrument was also limited by its size and by the effect the wind or observer’s motion would have on the plumb bob. To measure the sun angle, navigators held the instrument in front of them with the sun (slightly) to their side. For navigators on the deck of a moving ship, these limitations could be difficult to overcome.
Perspective Research Centre 
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