Learning Mathematics with yoga
ANGLES When two lines intersect at a point, the measure of the “opening” between these two lines is called an “Angle”. It is denoted by using the symbol ∠. Angles are usually measured in degrees and radians, which is a measure of circularity or rotation. Angles are a part of our day-to- day life. Engineers and architects use angles for the design of roads, buildings, and sporting facilities.
ANGLES The word ‘angle’ is derived from the Latin word ‘Angulus’, which means ‘an angle’. We come across different types of angles almost everywhere in our daily life. For example, the angle made by the hands of a clock, the angle made by two intersecting roads, the angle made by slice of Pizza, the angle made by the English Alphabet V, the angle made by the corner of the doors and windows and angles made by blades of a fan etc. We also use angles for navigation of planes and ships.
ANGLES IN EVERYDAY LIFE
Parts of an Angle In-plane geometry, an angle is formed when two rays are joined at their endpoints. There are different parts of the angle- 1.Two rays, which are called the sides of the angle. Look at the given image, sides OA and OB are sides of the angle AOB.
PARTS OF AN ANGLE 2. The vertex of the angle, which has a common endpoint that is shared by the two rays. Observe the given image below with two rays as ray 1 and ray 2 with one orange dot named as a vertex.
HOW TO LABEL ANGLES There are two main ways to label angles : 1.Give the angle a name usually a lowercase letter like a or b or sometimes a Greek letter like Alpha or theta 2.or by the three letters on the shape that define the angle with the middle letter being where the angle actually is (its vertex) 3.Example angle A is BAC and angle theta is BCD
MEASUREMENT OF AN ANGLE An angle is measured in degrees. One full rotation is equal to 360 degrees.
SIZE OF AN ANGLE The best way to measure the size of an angle is to use a protractor. The standard size of a protractor is 180°. There are two sets of numbers on a protractor: ● one in a clockwise direction ● another in an anti-clockwise direction
Types of Angles The angles can be classified into two main types: 1.Based on Magnitude 2.Based on Rotation
Types of Angles Based on Magnitude There are 7 types of angles based on the magnitude or measurements of an angle. 1. Zero Angle 2. Acute Angle 3. Right Angle 4. Obtuse Angle 5. Straight Angle 6. Reflex Angle 7. Complete/Full Angle
TYPES OF ANGLES
Zero Angle A zero angle (0∘) is an angle formed when both the arms of an angles are at the same position. PQ and PR are two rays originating from the same point and are in the same direction. So, they represent zero angle.
ZERO ANGLE WITH YOGA Parwani palak VITH A
EXAMPLES OF ZERO ANGLE The angle between hour and minute hand as shown in the clock below forms zero angle.
Zero ANGLES IN EVERYDAY LIFE
Acute Angle An acute angle is a type of angle whose measure is greater than 0∘ and less than 90∘. The figure illustrates an acute angle. Examples: 30∘,45∘,60∘ etc.
AcuteANGLE WITH YOGA Lalwani vinay VITH D Basantani jiya VITH B
Rajwani deepti VITH A Parwani palak VITH A
EXAMPLES OF ACUTE ANGLES The angle between hour and minute hand as shown in the clock below forms an acute angle. Also: the letter “A” has an acute angle
ACUTE ANGLES IN EVERYDAY LIFE
Right Angle A right angle is a type of angle whose measure is exactly equal to 90∘. The figure below illustrates a right angle.
Right ANGLE WITH YOGA Dayani bhavika VITH A ChanDnani vaibhav VITH A
Bahrani riya VITH A Parwani palak VITH A
EXAMPLES OF Right angles The angle between hour and minute hand as shown in the clock below forms the right angle. Never argue with a 90°angle, it is always right!
Right ANGLES IN EVERYDAY LIFE
Obtuse Angle An obtuse angle is a type of angle whose measure is greater than 90∘ and less than 180∘. The figure illustrates an obtuse angle. Examples: 100∘,120∘,150∘ etc.
Obtuse ANGLE WITH YOGA Ray soham VITH D Tanna bhakti VITH A
Kukreja riya VITH A Basantani jiya VITH B
EXAMPLES OF obtuse angles The angle between hour and the minute hand as shown in the clock below forms an obtuse angle.
Obtuse ANGLES IN EVERYDAY LIFE
Straight Angle A straight angle is a type of angle whose measure is exactly equal to 180∘. It is also called 180∘ angle. We can see, it is just a straight line, because the angle between its arms is 180∘. The figure illustrates a straight angle.
StraightANGLE WITH YOGA Parwani palak VITH A Shadija diya VITH A
Parwani palak VITH A
EXAMPLES OF straight angles The angle between hour and minute hand as shown in the clock below forms a straight angle.
Straight ANGLES IN EVERYDAY LIFE
Reflex Angle A reflex angle is a type of angle whose measure is greater than 180∘ and less than 360∘. The figure illustrates a reflex angle. Example: 200∘,220∘,250∘ etc.
Reflex ANGLE WITH YOGA Khemani muskan VITH A Thakur riddhi VITH A
EXAMPLES OF reflex Angles The angle between hour and minute hand as shown in the clock below forms a reflex angle.
Reflex ANGLES IN EVERYDAY LIFE
Complete/Full Angle A complete angle is a type of angle whose measure is exactly equal to 360∘. It is also called a full angle. The figure illustrates a complete/full angle.
EXAMPLES OF complete Angles The angle between hour and minute hand as shown in the clock below forms a complete angle.
Complete ANGLES IN EVERYDAY LIFE
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