Angles, well the name alone does half of the work of explanation. As evident from our previous reads, angles are nothing but the measure of separation between two sides. Now there are various kinds of angles present, a couple of which are listed below:
Adjacent angles: These are the angles which are present one after the other. In other words these are nothing but consecutive angles. There is no fixed measure for adjacent angles as it depends upon the individual angles.
Alternate interior angles: Imagine two parallel lines cut by a transversal. The angles in the inner part that is between the two parallel lines are known as interior angles. Now the angles which are opposite to each other between these two lines are known as alternate interior angles.
Relevance of angles:
A great deal of relevance of angles is witnessed in mathematical topics such as geometry, mensuration, trigonometry etc. Extensive use of angles, their different types and their properties is witnessed in topics that are mentioned above. For instance let us take the example of trigonometry. One cannot imagine the concept of trigonometry without the presence of a right angle. The very basis of trigonometry is from the 3 sides viz. hypotenuse, perpendicular and base. For determination of which side is which, the presence of a right angle is compulsory. Upon determination of these sides one can form the side ratios, the infamous Sin, Cos, Tan etc. Also there are various types of triangles named after the angles in them, let us see some of them:
Acute angled triangle: In an acute angled triangle all the angles measure less than 90 °. The sum of all of the angles is equal to 180 °.
Obtuse angled triangle: In an obtuse angled triangle one angle is greater than 90 ° in measure and the remaining two are less than 90 °. It is so as to have the sum of all angles as 180 °.
Right angled triangle: In a right angled triangle one of the angles is exactly equal to 90 ° in terms of measurement. Whereas the other two angles combined measure as 90 °. This makes up the fact that the sum of all three angles in a right angled triangle is equal to 180 °.
As we can see from the above three mentioned types of triangles, these triangles got their name entirely on the basis of the nature of the angles present in them. Such is the relevance and influence of angles in triangles.
Let us see some additional types of triangles:
Equilateral triangle: In an equilateral triangle all angles are equal in terms of measurement. As all the angles are equal, so all the sides are also equal in length. This is the direct result of the rule “Sides opposite to equal angles are also equal in terms of length”. The sum of all three angles in an equilateral triangle is exactly equal to 180 °. Since all angles in this kind of triangle are equal in measure, each angle measures 60 °.
Scalene triangle: In a scalene triangle all angles are unequal in terms of measure. There is no fixed value or any kind of constraint in the determination of the measure of angles. Sum of all angles here is 180 °.
These were some kinds of different triangles that exist. There are a number of different kinds of triangles that exist but are difficult to be mentioned here. Angles as a whole are of different types and of different kinds, if somewhere the measure is given in negative quantity that doesn’t mean the measure actually is in minus but the sense of measurement there is opposite.
Conclusion:
Close examination and scrutinizing of the details regarding angles, their types and their properties fetches us many unique insights. This makes us aware of the sheer importance and versatility of the different aspects of angles in mathematics.
Cuemath is the name whenever you face any problem in mathematics.
