Measurement of Angle
What is measurement of an angle?
Measurement of an angle is the quantification of the amount of rotation between two intersecting lines, rays, or line segments, at a common point.
The angle is formed at a vertex, when two line segments meet at a point.
The point is called vertex.
In the figure below
Measurement of an angle is the quantification of the amount of rotation between two intersecting lines, rays, or line segments, at a common point.
The angle is formed at a vertex, when two line segments meet at a point.
The point is called vertex.
In the figure below
- A is vertex
- \(\measuredangle ABC\) is an angle
- AB and CB are arms
System of measurement of Angle
What are the system of measurement of Angle?
There are three main systems used to measure angles: They are
There are three main systems used to measure angles: They are
- Degree system or Sexagesimal system
- Grade system or Centisimal system
- Radian system or circular system
What is degree system?
The degree system is a way to measure angles using a unit called a degree (°). In this system, a full circle is divided into 360 equal parts, so one complete turn is 360 degrees.
A straight angle (like a straight line) measures 180°, a right angle is 90°
In this system
The degree system is a way to measure angles using a unit called a degree (°). In this system, a full circle is divided into 360 equal parts, so one complete turn is 360 degrees.
A straight angle (like a straight line) measures 180°, a right angle is 90°
In this system
- a right angle = 90°
- 1°=60' (1 degree=60 minute)
- 1'=60'' (1 minute=60 seconds)
What is grade system?
The grade system is a way to measure angles using a unit called a degree (\(^g\)). In this system, a full circle is divided into 400 equal parts, so one complete turn is 400 grades. A straight angle (like a straight line) measures \(200^g\), a right angle is \(100^g\)
In this system
The grade system is a way to measure angles using a unit called a degree (\(^g\)). In this system, a full circle is divided into 400 equal parts, so one complete turn is 400 grades. A straight angle (like a straight line) measures \(200^g\), a right angle is \(100^g\)
In this system
- a right angle = \(100^g\)
- \(1^g\)=100' (1 grade=100 minute)
- 1'=100'' (1 minute=100 seconds)
What is radian system?
The radian system is a way of measuring angles based on the properties of a circle. Instead of dividing a circle into 360 degrees, the radian system relates the angle to the arc length of a circle.
In this system, one radian is the angle formed at the center of a circle when the length of the arc is equal to the radius of the circle.
The radian system is a way of measuring angles based on the properties of a circle. Instead of dividing a circle into 360 degrees, the radian system relates the angle to the arc length of a circle.
In this system, one radian is the angle formed at the center of a circle when the length of the arc is equal to the radius of the circle.
- a right angle = \(\frac{\pi}{2}\approx 1.57\) radian
- A straight angle =\(\pi \approx 3.14\) radian
- a full circle = \(2 \pi \approx 6.28\) radian
- Angle in radians \(\theta=\frac{l}{r}\)
Another way of measuring angle in radians is given by
\(\text{angle}=\frac{\text{arc length}}{\text{radius}}\) - So in radians, the angle around a complere circle is
\(\theta=\frac{l}{r}=\frac{2\pi(r)}{r}=2\pi\)
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