# UNIT 11. Angle.

# Unit 11. Angle - vocabulary.

∠ angle = two sides + the vertex |

A) acute angle < 90˚ B) right angle = 90˚ C) obtuse angle > 90˚ D) straight angle = 180˚ E) reflex angle > 180˚ F) one turn = 360 ˚
right angle = 90˚ acute (a), obtuse (b) and straight (c) angles reflex angle |

Two angles that sum to one right angle (90˚) are called The difference between an angle and a right angle is termed the
The complementary angles a and b (b is the complement of a and a is the complement of b).
Two angles that sum to a straight angle (180˚) are called The difference between an angle and a straight angle (180˚) is termed the
Here a and b are supplementary angles.
Two angles that sum to one turn (360˚) are called
Here the sum of the reflex angle and the acute angle makes an explementary angle. |

The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection. |

# Unit 11. Angle - reading.

*Angle.*

* The angle symbol ( ∠ ).*

In geometry, Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. According to Proclus an angle must be either a quality or a quantity, or a relationship. The first concept was used by Eudemus, who regarded an angle as a deviation from a straight line; The second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definition of right, acute and obtuse angles are certainly quantitative. Measuring angles. The size of a geometric angle is usually characterised by the magnitude of the smallest rotation that maps one of the rays into the other. Angles that have the same size are sometimes called congruent angles. In some contexts, such as identifying a point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing the cumalative rotation of an object in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of a full turn are not equivalent.
The measurement of angle In order to measure an angle The value of |

*Definitions, pictures and articles for reading adapted from:*