It is 90 degrees of the circle's circumference which has a full turn of 360 degrees.
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One-fourth of anything is always 25%.
A quadrant is a sector that equals 1/4 of a circle.
A circle comprises 360 degrees. So, a fourth of a circle is 360/4 = 90 degrees.
One half. The diameter of a circle is always twice the radius.
A full circle is 360o, so a quarter, (one fourth) of a circle is 90o.