What is Angle? — Mathematics

Definition 40.7 Primary & Middle School Mathematics · Chapter 40 — Lines, Circles and Angles

Two rays $[AB)$ and $[AC)$ with the same starting point $A$ form the angle $\widehat{BAC}$ ; the point $A$ is its vertex (always the middle letter!). Angles are measured in degrees ( $^\circ$ ), from $0^\circ$ to $360^\circ$ for a full turn. An angle is:

right if it measures $90^\circ$ ;
acute if it measures less than $90^\circ$ ;
obtuse if it measures between $90^\circ$ and $180^\circ$ ;
straight if it measures $180^\circ$ (the two rays form a line).

The four families of angles. The right angle (90) is the reference: acute means smaller, obtuse means larger. — The four families of angles. The right angle ( $90^\circ$ ) is the reference: acute means smaller, obtuse means larger.

Examples

Example 40.9

Before measuring, estimate! An angle slightly more open than the corner of a sheet of paper is a little over $90^\circ$ ; half a right angle is $45^\circ$ ; a third of a right angle is $30^\circ$ . If your protractor says $150^\circ$ for an angle that looks acute, you read the wrong scale: the correct measure is $180^\circ - 150^\circ = 30^\circ$ .

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Examples

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