Properties of Angles

Mathematics is a significant subject that helps in learning more about the world that we are a part of. Mathematics has a lot of topics and here we will be focusing on one such topic which is regarding the properties of angles. There are several properties and we will be focusing on them over here. Along with the properties, we will also focus on the topics such as parallel and transversal lines. 

Properties of Angles

There are various properties of angles. These can be regarding the supplementary angles, complementary angles, opposite angles, sum of interior angles in a triangle and a quadrilateral along with the corresponding and alternate angles. Along with the properties, a brief description of parallel lines and transversal lines are also shared. These topics are listed below: –

1. Property for right angles says that there is congruency in all the right angles.
2. Property of straight angles also states that there is congruency in all the straight angles.
3. According to the property of linear pair, if two angles are forming a linear pair then those angles are supplementary
4. Further, it can be said that there is congruency amongst the vertical angles as well.
5. In a triangle the total value of all three angles is one-eighty degrees and similarly, for a quadrilateral, it is three-sixty degrees. Now, in a triangle, there is a property regarding the exterior angle. As per this property, the value of an exterior angle in a triangle can be found as equal to the total value of the two non-adjacent interior angles. Further, the value of either non-adjacent interior angle of a triangle is less than the value of the exterior angle of the triangle.
6. In opposite angles, two intersecting lines lead to the formation of four angles wherein each angle is opposing the other one such that they form opposite angles.
7. In two parallel lines, one can observe that the corresponding angles are also equal in nature. 
8. Further, if the two lines are parallel to each other then alternate angles can also be equal. 

It can be concluded that the above eight points can help one learn a lot about the properties of angles.

Apart from all these topics, some other important concepts include parallel lines, adjacent angles and transversal. One can say that those lines which are equidistant from each other and do not intersect with one another can be called parallel lines. On the other hand, transversal can be explained as that line which is intersecting two or even greater than two lines. Lastly, adjacent angles can be explained as those angles which are having a common side along with having a common vertex. 

Thus, these are a few important points that help in learning more about angles. 

Half Angle Formula

In trigonometry, half-angle formulas are studied. By the means of double angle formulas, one can find out about the half-angle formulas. To learn about the value of various trigonometry related functions such as Sin22.5 degrees and many more we can try using half-angle formulas. 

Conclusion

Thus, as observed from the above section, we gained more clarity about not just half-angle formulas but also the diverse properties of angles. Angles have a lot of different properties. In the above section, there were various topics very well covered in a comprehensive manner such as complementary angles, adjacent angles, opposite angles, supplementary angles, the sum of interior angles. Apart from all these insightful topics, we also learnt about the concept of parallel lines and transversal lines. It can be concluded, that the above section helped in gaining an insight into the various properties of angles and the half-angle formula as well.