How many degrees are in a right angle?

A right angle is 90 degrees, exactly a quarter of a full turn. The choice of 360 degrees for a complete circle is inherited from Babylonian mathematics, which counted in base sixty, and it survives because 360 divides evenly by so many numbers, including 2, 3, 4, 5, 6, 8, 9, 10 and 12, which makes fractions of a circle come out as whole numbers. Right angles are the backbone of practical geometry: two lines meeting at 90 degrees are perpendicular, the corners of squares and rectangles are right angles, and Pythagoras's theorem only applies to triangles containing one. Builders check a corner with the three-four-five rule, since a triangle with sides in that ratio must contain a right angle. In a triangle the angles always sum to 180 degrees, so a right-angled triangle has exactly 90 degrees left to share between its other two corners, meaning it can never contain more than one.

Mathematicians often measure angles in radians instead, where a right angle is pi over two.