Vertical angles

Vertical angles

The vertical angles refer to the angles which are opposite to that of each other in the event of intersection of two lines. They can be stated to be equal and “vertical” is indicative of vertex and they are also known as the vertically opposite angles. The vertical angles are indicative of pair angles which are formed owing to intersection of the two lines. The vertical angles are indicative of vertically opposite angles as the angles are found to be lying opposite to that of each other. There exist real-life settings in which the vertical angles are found to include for example sign of the railroad crossing. The Egyptians used to draw the two intersecting lines and they used to measure vertical angles for conforming that both of them have been equal. The vertical angles can be said to be equal to that of one another and two pairs of the vertical angles can be formed when there is intersection of two lines.

Vertical angles theorem

The vertical angles theorem refers to the two opposite angles which are formed owing to their intersection and they are always found to be congruent to each other. The vertical angles proof can be said to be simple and it is formed on the basis of straight lines. The angles within the straight line can be said to add up to that of 180 °.

The angle 1 and angle 2 will sum up to form 180 ° and on the other hand the sum of angle 1 and 4 will become 180 °. They are linear pair of the angles and it can be brought out that angle 1 and angle 2 would be equal to 180 ° which would be equal to angle 1 and angle 4. For finding measure of angles in the figure, straight angle property would be used and alongside with it the vertical angle theorem would be made use of simultaneously.

Vertical angles proof

The vertical angles theorem brings out that opposite angles of the two intersecting lines can prove to be congruent. The proof can be said to be simple and it is found to start in the event of knowing about the straight lines and the angles. The angle addition postulate can be made use of and substitution property of the equality can be used for arriving at the conclusion. The angle addition postulate helps in bringing out that the two adjacent angles would form the straight angle and two lines would be able to add up to 180 °.

It can hence be stated that in terms of the substitution,  a is greater than m and c on the other hand is greater than m which can be effective in replacing the 180 degrees in equation towards the bottom.

Vertical angles

Complementary angles

The vertical angles and the complementary angles can be made use of for the calculation of the unknown angle measurements. The sum of the two angles being 90 degrees, it can be termed as the complementary angles.

Congruent angles

The two angles can be stated to be congruent in the event of corresponding sides and the angles being of the equal measure. The two angles can become congruent in the event of coinciding when they have been superimposed. The process of turning in and by moving out they can aid to coincide with that of each other.

Intersecting and the non-intersecting lines

The parallel lines getting crossed by another line can be termed as the transversal. These angles can help to form pairs of the angles and they possess special names.

Angles

The dynamic notion of the angles is found to involve an action and rotation which exists in between the two lines. The angle as the measure can be conceived to be length of the circular arcs or ratio existing in between various areas of the circular sectors. It is thought of as having the geometric shape and angle can be said to be delineation of the space which takes place with the aid of two intersecting lines. The each of the perspectives can be said to carry the methods that can help to check the angle congruency.

Vertically opposite angles

The vertical angles are found to intersect each other and opposite angles are formed owing to intersection which are called the vertical angles or the vertically opposite angles. The pair of the vertically opposite angles are found to be equal to that of each other. The vertical angle and the adjacent angle are found to be the supplementary angles and they can help to make up the 180 degrees. The two lines meeting at point in the plane can be called the intersecting lines.

Examples of vertical angles

The line “C” are found to intersect the two lines- a and the b. The vertical angles are found to be formed within each intersection. The vertical pairs of the angles are called :

1 and 6

2 and 5

3 and 8

4 and 7

Practical Questions on Vertical Angles

How value of vertical angle can be measured?

The vertical angles in between the instruments and their points can be measured which can help to solve the unique purpose. The points lying on same side of horizontal, vertical angle in between points can be stated to be difference in between measured angles. They can lie on either side of horizontal with the aid of instrument and vertical angle in between points can act as sum of angles which have been measured.

Are vertical angles always congruent?

The vertical angles can be stated to be congruent and it signifies that they can prove to be equal. The two angles being the vertical angles thenceforth the angles can be stated to be congruent.

Can the vertical angles be adjacent?

The adjacent angles can also be stated to be the vertical angles as they are found to share same vertex and they are formed in the event of two lines crossing. The sum of the adjacent angles being equal to that of 90 °it can be stated to be complementary. The sum of the adjacent angles being equal to that of 180 ° it can be stated to be supplementary. The adjacent angles can be said to be formed when one pair of the vertical angles are found to merge with that of another angle from another pair.