# Angles* Angle. Degree and radian measures of an angle. * Right (direct), acute and obtuse angle. Mutually perpendicular straight lines. Signs of angles. Supplementary (adjacent) angles. Vertically opposite (vertical) angles. Bisector of an angle. *Angle * is a geometric figure ( Fig.1 ), formed by two rays OA and OB ( *sides of an angle *), going out of the same point O (a *vertex of an angle*).
An angle is signed by the symbol and three letters, marking ends of rays and a vertex of an angle: AOB (moreover, a vertex letter is placed in the middle). A *measure of an angle* is a value of a turn around a vertex O, that transfers a ray OA to the position OB. Two units of angles measures are widely used: a *radian *and a *degree*. About a radian measure see below in the point "A length of arc" and also in the section "Trigonometry". A *degree measure. *Here a unit of measurement is a *degree *( its designation is ° or *deg *) *– *a turn of a ray by the 1/360 part of the one complete revolution. So, the complete revolution of a ray is equal to 360 deg. One degree is divided by 60 *minutes *( a designation is ‘ or *min *); one minute – correspondingly by 60* seconds * ( a designation is “ or *sec *).An angle of 90 deg ( Fig.2 ) is called a * right * or *direct* angle; an angle lesser than 90 deg ( Fig.3 ), is called an *acute*angle; an angle greater than 90 deg ( Fig.4 ), is called an *obtuse* angle.
Straight lines, forming a right angle, are called *mutually perpendicular *lines. If the straight lines AB and MK are perpendicular, this is signed as: AB MK. *Signs of angles. * An angle is considered as *positive*, if a rotation is executed *opposite a clockwise* , and *negative* – otherwise. For example, if the ray OA displaces to the ray OB as shown on Fig.2, then AOB = + 90 deg; but on Fig.5 AOB = – 90 deg.
*Supplementary (adjacent) angles* ( Fig.6 ) – angles AOB and COB, having the common vertex O and the common side OB; other two sides OA and OC form a continuation one to another. So, a sum of supplementary (adjacent) angles is equal to 180 deg.
*Vertically opposite (vertical) angles * ( Fig.7) – such two angles with a common vertex, that sides of one angle are continuations of the other: AOB and COD ( and also AOC and DOB ) are vertical angles.
A* bisector* of an angle is a ray, dividing the angle in two ( Fig.8 ). Bisectors of vertical angles (OM and ON, Fig.9) are continuations one of the other. Bisectors of supplementary angles (OM and ON, Fig.10) are mutually perpendicular lines.
*The property of an angle bisector:**any point of an angle bisector is placed by the same distance from the angle sides*.
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