A degree is a unit used to represent the measurement of an angle. Angles are usually measured in radians and degrees. In the case of practical geometry, we always use degrees as a unit of an angle. A degree is represented by ° (degree symbol).
|1.||Definition of Degree|
|2.||Measuring Angles in Degrees|
|3.||Solved Examples on Degrees|
|4.||Practice Questions on Degrees|
|5.||FAQs on Degrees|
Definition of Degrees
The unit of measure for an angle in mathematics is called a degree. The degree of an angle is measured by using a tool called a protractor. A complete circle rotates at 360° and angles can be measured at different angles showcasing different degrees such as 30°, 45°, 60°, and so on. One rotation is divided into 360 equal parts, and each part is called a degree. We denote a degree with a circle °. For example, 180° means 180 degrees.
Degrees and Radians
Angles are measured not only in degrees but also in radians. Radian is made by wrapping a radius along the circle. One complete counterclockwise revolution, in radians, is equal to 2π. We can convert the degree to radians and radians to degrees by using the following two formulas:
- To convert radians to degrees the formula is [Degrees = Radians × 180 / π]. One Radian is about 57.2958 degrees.
- To convert degrees to radians the formula is [Radians = Degrees × π / 180].
Given below is a table showing equivalent radian values for respective degrees:
Measuring Angles in Degrees
The best tool to measure angles in degrees is a protractor. The curved edge of the protractor is divided into 180 equal parts.
There are two sets of numbers on a protractor:
- One in a clockwise direction
- Another in a counter-clockwise direction
If you look closely, the protractor has degrees marked from 0 ° to 180 ° from left to right on the outer edge and 180 ° to 0 ° on the inside.
Internal reading and external reading supplement each other. i.e., they add up to form a 180° degree angle.
Look at the above image, if the measured angle is on the left side from the center of the protractor, we will focus on the external readings of the protractor. In this case, ∠POR lies on the left side therefore ∠POR = 80°.
If the measured angle is on the right side of the protractor, we will focus on the internal readings of the protractor. In this case, ∠QOR lies on the right side therefore, ∠QOR = 100°.
Here we have another example of measuring angle in degrees. Let's try to measure the angle ∠AOB in the figure given below with the help of a protractor.
Step 1:Hold the protractor in such a way that the midpoint of the protractor coincides with vertex O of the given figure. Align the protractor perfectly with the ray OB as shown below.
Step 2: Start reading from the 0° mark on the bottom-right of the protractor. Measure the angle using the internal readings on the lower arc of the protractor.
Therefore, ∠AOB = 37°.
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Solved Examples on Degrees
Example 1: Find the total number of degrees in three straight angles?
Solution: One straight angle = 180 degrees.
Three straight angles = one and a half full rotations
= 360 + 180 = 540 degrees.
Another approach to find the number of degrees in three straight angles = 3 × 180° = 540°.
Hence, with both the methods answer is same.
The three straight angles = 540 degrees.
Example 2: Emma and James are cutting papers with the help of scissors to build some designs. James observes that during the cutting process, scissors make an angle. He asked Emma what the angle is in degree formed between the two arms of the given pair of scissors? Can you help her?
Solution: Place the protractor along one arm and measure the angle in degrees.
The angle which is to be measured is at the left part of the protractor.
Therefore, use the outer readings of the protractor.
Therefore, Angle formed = 30°
Example 3: Help Jack to convert the 60-degree angle into radians.
Solution: The formula for the conversion of degree into radians is, 1 degree = π/180 rad
Now multiply 60 on both sides,
1 degree = π/180 rad
60 × degree = π/180 × 60° rad
= π/3 rad
= 1.047 rad
Therefore, 60 degrees = 1.047 rad
FAQs on Degrees
What is 1 Degree in Radians?
1 degree = π/180 radians
= 0.0174533 radians
How do you Define a Degree?
A degree, usually indicated by ° (degree symbol), is a measure of the angle. Angles can be of different measures or degrees such as 30°, 90°, 55°, and so on. To measure the degree of an angle, we use a protractor.
What Tools are Used to Measure the Degree of Angles?
There are 5 Types of Tools to Measure Angles:
- Angle Gauge
- Multiple Angle Measuring Ruler
- Try Square
- Sine Bar
How Many Degrees Are in a Half Turn?
Half-turn means making a straight angle. The measurement of a straight angle is 180°. Therefore, in half-turn, there are 180 degrees.
How Many Degrees are in a Full Turn?
Full-turn means making a completer angle. The measurement of a complete angle is 360°. Therefore, in one full turn, there are 360 degrees.
What is a Degree in Math Geometry?
A degree is a unit. While measuring any angle we use the degrees symbol to denote it. It is denoted by °. For example, one full rotation is 360 degrees or (360°). One degree is equivalent to π180 radians.
What are the Different Degrees of Angles we see in Geometry?
There are different types of angles according to their degrees in geometry. Let us see what they are:
- Right Angle - Measurement of the right angle is 90 degrees (90°).
- Obtuse Angle - Measurement of an obtuse angle is greater than 90° and lesser than 180°
- Straight Angle - The Measurement of straight angle is 180°
- Reflex Angle - Measurement of the reflex angle is greater than 180° and lesser than 360°.