Hello Friends, in today's session we all are going to discuss about some of the most interesting topics of mathematics, angles and types of angles which are usually studied in Grade III. Here I am going to tell you the best way of understanding these terms.
Angle is formed when two rays starts from same point. Angles are the part of geometry shapes and the measuring unit of angles is degree. The point of meeting of rays is also known as vertex. Angles are usually assumed in 2D planes but they also presents in 3D planes. Two angles can be concurrent to each other only when they are identical in degree and the transformation of one angle from another completely overlap the another one. The size of angle is measured by the rotation of one ray away or towards the other one, therefore the angle is basically identified by the degree of rotation of rays. More more information read this resource.
To measure an angle a circular arc is drawn between two rays at the vertex with the help of compass. We can use the formula i.e.
ÆŸ = k q
p
Here ‘q’ is the length of arc drawn and ‘p’ is the distance of the arc from the point of meeting of rays also called as radius of circle and the last ‘k’ is known as the scaling constant which depends on the measurement unit chosen. From the above example we can conclude that ‘ÆŸ’ is independent of the arc size and the ‘q’ directly depends upon the ‘r’.
Now let’s move on types of angle:
What is an Acute Angle: Acute angle can be defined as the angle which is less than 90 degree.
Right angle: Right angle can be defined as the angle which is equal to 90 degree.
Obtuse angle: Obtuse angle can be defined as the angle which is greater than 90 degreebut less than 180 degree i.e. angle must be between 90 to 180 degrees.
Straight angle: Straight angle can be defined as the angle which is equal to 180 degree. Therefore these types of angles look like straight lines.
Reflex angle: Reflex angle can be defined as the angle which is greater than 180degree but less than 360 degrees i.e. between 180 and 360 degrees.
Adjacent angles: Adjacent angles can be defined as the angles which have common vertex and a common side.
Complementary angles: Complementary angles can be defined as the angles whose sum is equal to 90 degree and all together form a right angle.
Supplementary angles: Supplementary angles can be defined as the angles whose sum is equal to 180 degree.
Vertical angles: Vertical angles can be defined as the angles which have common vertex and their sides are formed by same lines and are opposite to each other.
When two parallel lines are intersected by the third line, eight angles are formed. Four of them are alternate interior angles and the remaining four are alternate exterior angles.
Alternate interior angles are pairs of angles on the inner side of the two parallel lines.
Alternate exterior angles are pairs of angles on the outer side of the two parallel lines.
Corresponding angles are pairs of angles which are similar in position and have face towards the same direction.
In upcoming posts we will discuss about Expanded Notation in Grade III and online math tutor help. Visit our website for information on CBSE board home science syllabus for class 11
Angle is formed when two rays starts from same point. Angles are the part of geometry shapes and the measuring unit of angles is degree. The point of meeting of rays is also known as vertex. Angles are usually assumed in 2D planes but they also presents in 3D planes. Two angles can be concurrent to each other only when they are identical in degree and the transformation of one angle from another completely overlap the another one. The size of angle is measured by the rotation of one ray away or towards the other one, therefore the angle is basically identified by the degree of rotation of rays. More more information read this resource.
To measure an angle a circular arc is drawn between two rays at the vertex with the help of compass. We can use the formula i.e.
ÆŸ = k q
p
Here ‘q’ is the length of arc drawn and ‘p’ is the distance of the arc from the point of meeting of rays also called as radius of circle and the last ‘k’ is known as the scaling constant which depends on the measurement unit chosen. From the above example we can conclude that ‘ÆŸ’ is independent of the arc size and the ‘q’ directly depends upon the ‘r’.
Now let’s move on types of angle:
What is an Acute Angle: Acute angle can be defined as the angle which is less than 90 degree.
Right angle: Right angle can be defined as the angle which is equal to 90 degree.
Obtuse angle: Obtuse angle can be defined as the angle which is greater than 90 degreebut less than 180 degree i.e. angle must be between 90 to 180 degrees.
Straight angle: Straight angle can be defined as the angle which is equal to 180 degree. Therefore these types of angles look like straight lines.
Reflex angle: Reflex angle can be defined as the angle which is greater than 180degree but less than 360 degrees i.e. between 180 and 360 degrees.
Adjacent angles: Adjacent angles can be defined as the angles which have common vertex and a common side.
Complementary angles: Complementary angles can be defined as the angles whose sum is equal to 90 degree and all together form a right angle.
Supplementary angles: Supplementary angles can be defined as the angles whose sum is equal to 180 degree.
Vertical angles: Vertical angles can be defined as the angles which have common vertex and their sides are formed by same lines and are opposite to each other.
When two parallel lines are intersected by the third line, eight angles are formed. Four of them are alternate interior angles and the remaining four are alternate exterior angles.
Alternate interior angles are pairs of angles on the inner side of the two parallel lines.
Alternate exterior angles are pairs of angles on the outer side of the two parallel lines.
Corresponding angles are pairs of angles which are similar in position and have face towards the same direction.
In upcoming posts we will discuss about Expanded Notation in Grade III and online math tutor help. Visit our website for information on CBSE board home science syllabus for class 11
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