What Is Vertical Angles Theorem

Vertical Angles

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other. In other words, whenever two lines cantankerous or intersect each other, iv angles are formed. We can find that two angles that are opposite to each other are equal and they are called vertical angles. They are also referred to every bit 'Vertically opposite angles' every bit they lie opposite to each other.

1.	What are Vertical Angles?
two.	Vertical Angles Theorem
3.	Vertically Opposite Angles Worksheet
iv.	FAQs on Vertical Angles

What are Vertical Angles?

When 2 lines intersect, four angles are formed. At that place are two pairs of nonadjacent angles. These pairs are chosen vertical angles. In the prototype given below, (∠1, ∠three) and (∠2, ∠4) are 2 vertical bending pairs.

Vertical Angles Definition

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In unproblematic words, vertical angles are located across from ane some other in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles every bit they are situated opposite to each other.

Vertical Angles

Vertical Angles Theorem

Vertical angles theorem or vertically opposite angles theorem states that 2 contrary vertical angles formed when ii lines intersect each other are always equal (congruent) to each other. Allow'south learn virtually the vertical angles theorem and its proof in detail.

Statement: Vertical angles (the opposite angles that are formed when two lines intersect each other) are congruent.

Vertical Angles Proof

The proof is simple and is based on directly angles. We already know that angles on a straight line add up to 180°.

Vertical Angles Theorem

So in the above figure,
∠1 + ∠ii = 180° (Since they are a linear pair of angles) --------- (1)
∠ane +∠4 = 180° (Since they are a linear pair of angles) --------- (two)
From equations (1) and (2), ∠1 + ∠ii = 180° = ∠i +∠4.
Co-ordinate to transitive belongings, if a = b and b = c so a = c.
Therefore, we tin can rewrite the statement every bit ∠1 + ∠2 = ∠1 +∠4. --------(iii)
Past eliminating ∠ane on both sides of the equation (iii), we get ∠2 = ∠4.
Similarly. we can use the same set of statements to prove that ∠1 = ∠3. Therefore, nosotros conclude that vertically reverse angles are always equal.

To detect the measure of angles in the effigy, we utilize the straight angle property and vertical angle theorem simultaneously. Let us look at some solved examples to understand this.

Vertically Reverse Angles Worksheet

The post-obit table is consists of artistic vertical angles worksheets. These worksheets are easy and complimentary to download. Try and practice few questions based on vertically opposite angles and enhance the knowledge almost the topic.

Important Notes

Vertical angles are always equal.
Vertical angles can be supplementary equally well as complimentary.
Vertical angles are always nonadjacent.

Topics Related to Vertical Angles

Check out some interesting manufactures related to vertical angles.

Angles
Alternating Angles
Alternate Interior Angles Theorem
Complementary Angles
Complementary Bending Calculator
Supplementary Angles
Geometry

Vertical Angles Examples

Example 1: Notice the measure of ∠f from the figure using the vertical angles theorem.

Solution:

In the image given below, we can discover that AE and DC are ii directly lines. Here, ∠DOE and ∠AOC are vertical angles.

∠DOE = ∠AOC

118° = ninety° + ∠f

∠f = 118° - 90°

∠f = 28°

Therefore, ∠f = 28°
Instance ii: In the figure shown below ∠f is equal to 79° because vertically opposite angles are equal. Is the statement correct? Justify your answer.

Solution:

Hither, 79° and f are located opposite, but they are not vertical angles as the angles are non formed by the intersection of two straight lines. Here, BD is not a straight line. Therefore, ∠f is not equal to 79°. The given statement is false.
Case three: If angle b is 3 times the size of bending a, observe out the values of angles a and b by using the vertical angles theorem.

Solution:

From the figure, we tin find that lxxx° and the sum of the angles a and b are vertically reverse. Which ways ∠a + ∠b = lxxx°. Information technology is given that ∠b = 3∠a. Substituting the values in the equation of ∠a + ∠b = 80°, we get, ∠a + three∠a = fourscore°

4∠a = eighty°

∠a= 80°/4

∠a= 20°

Since ∠b = three∠a, ∠b = three × 20°

∠b = sixty°

Therefore, ∠a= 20° and ∠b= 60°

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FAQs on Vertical Angles

What are Vertical Angles in Geometry?

Vertical angles are formed when 2 lines intersect each other. Out of the four angles that are formed, the angles that are opposite to each other are vertical angles. They are as well referred to every bit 'vertically opposite angles. These angles are ever equal.

☛Also Read

Pairs of Angles
Transversals and Related Angles
Interior Angles

Are Vertical Angles Congruent?

When two directly lines intersect each other vertical angles are formed. Vertical angles are always congruent and equal. Vertical angles are congruent as the 2 pairs of non-adjacent angles formed by intersecting two lines superimpose on each other.

☛Check out and read

Congruent Angles
Coinciding
Coinciding Triangles

Are Vertical Angles Supplementary?

When whatever ii angles sum up to 180°, we call them supplementary angles. If there is a case wherein, the vertical angles are right angles or equal to 90°, then the vertical angles are 90° each. Therefore, the sum of these two angles volition be equal to 180°. Then in such cases, nosotros tin say that vertical angles are supplementary. It is to be noted that this is a special case, wherein the vertical angles are supplementary. Otherwise, in all the other cases where the value of each of the vertical angles is less than or more than than 90 degrees, they are not supplementary.

☛Cheque out the difference betwixt the following:

Supplementary Angles
Complementary Angles
Linear Pair of Angles

What is the Vertical Angle Theorem?

The vertical bending theorem states that the angles formed by 2 intersecting lines which are called vertical angles are congruent. The vertical angles are of equal measurements. For instance, If ∠a, ∠b, ∠c, ∠d are the 4 angles formed by ii intersecting lines and ∠a is vertically opposite to ∠b and ∠c is vertically contrary to ∠d, and so ∠a is coinciding to ∠b and ∠c is coinciding to ∠d.

Tin Vertical Angles Exist Right Angles?

Yep, vertical angles can exist right angles. When the two contrary vertical angles measure xc° each, and then the vertical angles are said to be correct angles. This tin can be observed from the ten-axis and y-axis lines of a cartesian graph.

☛Cheque out

Right Angle
90 Degree Bending
180 Caste Angle

How to Measure the Value of Vertical Angle?

While solving such cases, showtime we need to observe the given parameters carefully. If the angle adjacent to the vertical angle is given then it is piece of cake to determine the value of vertical angles past subtracting the given value from 180 degrees to As it is proved in geometry that the vertical angle and its adjacent angle are supplementary (180°) to each other.

How do yous tell if an Bending is an Side by side or Vertical Angle?

Vertical angles are the angles formed when 2 lines intersect each other. The reverse angles formed by these lines are called vertically reverse angles. Whereas, adjacent angles are ii angles that take i common arm and a vertex.

Tin Vertical Angles Be Adjacent?

Vertical angles are reverse from each other whereas, side by side angles are the ones next to each other. Thus, vertical angles tin can never exist adjacent to each other.

Are Vertical Angles Always Congruent?

Yes, vertical angles are ever congruent. The intersection of two lines makes iv angles. In this, two pairs of vertical angles are formed. They are equal in measure and are congruent.