Angle
An angle is created when two lines or rays intersect at a place. Angles have a common point known as the vertex, and they have lines or rays known as the sides.
The symbol for an angle is, ‘∠’ and it is measured in degrees. The symbol for degrees is, ‘°’.
We can write ∠B as “∠ABC” or “∠CBA”.
The sides of ∠ABC are AB and BC.
180 degree angle
A 180 degree angle is the measurement of an angle when the sides are on opposite sides of the vertex, and on form a straight line. A straight angle’s vertex angle is 180° in measure.
Here, ∠AOB = 180°.
∠AOB can therefore be considered to be a straight angle.
Examples of 180 Degree Angles in Everyday Lives
- The see-saw creates a 180 degree angle.
- A straight stick serves as a representation of a 180 degree angle.
- A flat surface has a 180° angle.
- An analog timepiece shows a straight angle at 6:00 a.m.
Different types of Angles
On the basis of their measurement, we can categorize angles.
Acute Angle:
An acute angle is one with a measure of less than 90 degrees. 45°, for instance.
Right Angle:
The angle with a 90° measurement.
Obtuse Angle:
An angle with a measure of more than 90° but less than 180° is said to be obtuse. 120°, for instance.
Straight Angle:
An angle with a measure of 180 degrees.
Reflex Angle:
An angle that is larger than 180° but smaller than 360°. 270°, for instance.
Complete Angle:
An angle with a measure of 360 degrees.
Solved Examples
Example 1: On a clock, the hour hand is at ‘6’ and the minute hand is at ‘12’. What is the angle formed between the hour hand and the minute hand?
Solution:
If the hour hand of a clock is at 6 and the minute hand is at ‘12’, the time is 6:00. Both hands form a straight line, the angle between them is a straight angle, that is 180°.
Example 2: Find out the straight angle pairs from a given figure.
Solution:
Two angles combined to form a straight angle are called straight angle pairs.
∠COA + ∠DOA = 180°
∠AOD + ∠BOD = 180°
∠DOB + ∠COB = 180°
∠BOC + ∠AOC = 180°
Example 3: If a 180-degree angle is divided into two parts, and one part measures 80 degrees, then what is the measure of other parts?
Solution:
Let the unknown angle be x and the given angle is y = 80°.
x + y = 180°
x + 80° = 180°
x = 180° – 80° = 100°
Therefore, the angle measure of the other part is 100°. It is an obtuse angle.
Example 4: There angles formed a straight angle together – angle A, angle B, and angle C. If angle A = 40 degrees, angle B = 60 degrees, then what is the measurement of angle C?
Solution:
We know that a straight angle is 180 degrees .
This implies, angle A + angle B + angle C = 180 degrees.
40° + 60° + C = 180°
C = 180° – 100° = 80°
Therefore, the measurement of angle C is 80°.
The 180-degree angle can be drawn with the help of a protractor and compass.
A straight angle is 180°.
A right angle, or 90°, is the half of a straight angle.
Angles include acute, obtuse, right, reflex, and full angles.
To create a straight angle, we can unite two right angles.
A full angle consists of two straight angles.
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The table of 28 is also known as the multiplication table of 28. It shows us the values that we obtain by multiplying 28 with natural numbers. The table of 28 can be written using two operations – multiplication and addition.