Measurement & Data
Understanding Angles
Understanding an angle as a rotation, measured as a fraction of a circle.
Measuring a Turn
An angle measures an amount of turning between two rays that share a starting point. The unit used to measure that turn is the degree, based on dividing one full turn around a circle into 360 equal parts.
Definition — Degree
Because an angle measures a fraction of a full circle, larger fractions of the circle produce larger angle measures. A right angle, exactly a quarter of a full turn, measures 90 degrees since 360 ÷ 4 = 90.
Worked Example — Finding an Angle as a Fraction of a Circle
Worked Example — Classifying an Angle by Its Measure
Geometry Canvas
Construct
Objects
- 1.
P1: a free point, draggable on the plane
- 2.
P2: a free point, draggable on the plane
- 3.
P3: a free point, draggable on the plane
- 4.
poly1: the polygon through P1, P2, P3
Measurements
- poly1area = 15perimeter = 17.66
Tip
Common Mistakes
Judging an angle's size only by how long its two rays are drawn, rather than by the actual amount of turn between them.
An angle's measure depends only on how much the rays turn away from each other, not on how long the rays are drawn — a short-armed and long-armed angle can have the exact same measure.
Mixing up acute and obtuse, such as calling an angle smaller than 90 degrees obtuse.
An acute angle measures less than 90 degrees (a smaller turn than a right angle); an obtuse angle measures more than 90 but less than 180 degrees (a larger turn than a right angle).
Key Takeaways
- An angle measures an amount of turning between two rays, in units called degrees.
- A full circle measures 360 degrees; a right angle measures exactly 90 degrees.
- An angle can be classified as acute (less than 90°), right (exactly 90°), or obtuse (between 90° and 180°).
Summary
Understanding an angle as a fraction of a full circle's rotation gives degree measurement real meaning. The next lesson puts that understanding to practical use, measuring and drawing angles with a protractor.
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