Degree (angle measure)

High School

Definition

Indicated in math by the ° symbol. It is a unit for measuring angles (not to be confused with the degree that measures temperature and also uses the same symbol). It takes 360 degrees to make a full rotation in a circle. Each degree is equal to \(1 \over 360\) of a revolution. Degrees are usually measured using a protractor.

Worked examples

\(90^\circ\) is a right angle, \(180^\circ\) is a straight line, \(360^\circ\) is a full rotation

These are the benchmark angles you'll see everywhere in geometry.

\(\frac{1}{4} \times 360^\circ = 90^\circ\)

A quarter turn is one-fourth of a full rotation, so it measures 90 degrees.

Common mistakes

\(180^\circ\) is a full circle → \(360^\circ\) is a full circle; \(180^\circ\) is a straight angle Students often halve the total by mistake—remember a full rotation is 360 degrees.
measuring from the wrong scale on the protractor → always read from the scale that starts at 0° on your angle's baseline Protractors have two scales; pick the one where the first ray aligns with zero.
writing \(90\) instead of \(90^\circ\) → \(90^\circ\) Always include the degree symbol to show you are measuring an angle, not a plain number.

Where you'll use it next

Degrees are fundamental in geometry for classifying triangles and polygons, in trigonometry for sine and cosine, and in coordinate transformations and rotations in pre-calculus and physics.

Found in 1 StudyPug lesson

Converting between degrees and radians

Grade 12 Math

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