UNITS OF MEASUREMENTS OF ANGLES
Types of Angles :
Acute angles : An angle whose measure is less than \(90^0\) and greater than \(0^0\) is called an acute angle i.e., if is an acute angle, then \({0^0} < \theta < {90^0}\)
Right angle : An angle whose measure is \(90^0\) is called a right angle.
Obtuse angle : An angle whose measure is greater than\(90^0\) and less than \(180^0\) is called obtuse angle.
Straight angle : An angle whose measure is \(180^0\) is called a straight angle
Note : A straight angle = two right angles.
Reflex angle : An angle whose measure is greater than \(180^0\) and less than \(360^0\) is called a reflex angle.
Complete angle : An angle whose measure is \(360^0\) is called a complete angle.
Here \(\angle AOB\) is \(360^0\)
Note : A complete angle = Four right angles = Two straight angles
Zero angle : If the measure of the angle is zero, it is called a zero angle
There are three different systems for measuring angles.
i) Sexagesimal system or British system : The Sexagesimal system is the most prevalent system of measurement where a right angle is divided into 90 equal parts called Degrees. Each degree is divided into 60 equal parts called Minutes, and each minute into 60 equal parts called Seconds.
The symbols \({1^0},{1^1}and{1^{11}}\) are used to denote a degree, a minute and a second respectively
In short,
1 right angle = 900(or 90 degrees)
10(or 1 degree) =601 (or 60 minutes)
11(or 1 minute) =6011 (or 60 seconds)
ii) Centesimal system or French System : In the Centesimal system, the right angle is divided into 100 equal parts, called Grades; each grade is subdivided into 100 minutes, and each minute is subdivided into 100 seconds.
The symbol is used to denote a grade.
In short,
900 (or 1 right angle) =100g (100 grades)
1g (or 1 grade) =1001 (or 100 minutes)
11 (or 1 minute) =10011 (or 100 seconds)
Note : It is clear that minutes and seconds in sexagesimal and centesimal systems are different.
iii) Circular System or Radian Measure :In the circular system, the radian measure of an angle is introduced using arc lengths in a circle of radius r.