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# Vertical Angles

Vertical angles are formed when two lines intersect. They are the pair of opposite angles that are across from each other and have a common vertex

• Vertical Angles
• Formula for Vertical Angles
• Solved Examples
• FAQs

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## Vertical Angles

Vertical angles are formed when two lines intersect. They are the pair of opposite angles that are across from each other and have a common vertex (the point where the two lines intersect).

Vertical angles are always congruent, meaning that they have the same measure. In other words, if angle A and angle B are vertical angles, then angle A is congruent to angle B.

Vertical angles are also sometimes called opposite angles or vertically opposite angles. An important property of vertical angles is that they are always equal in measure, no matter how the intersecting lines are oriented. ## Formula for Vertical Angles

There is no specific formula for vertical angles, but the key property of vertical angles is that they are always congruent.

This means that if we have two intersecting lines and we label the angles formed as A, B, C, and D (as shown in the diagram below), then we have the following relationships:

Angle A is congruent to angle C

Angle B is congruent to angle D

Angle A + angle B = 180 degrees (because they form a straight line)

Angle C + angle D = 180 degrees (because they form a straight line)

In summary, the formula for vertical angles is that they are always congruent to each other. Additionally, because vertical angles are formed by intersecting lines, we can use properties of lines and angles (such as the fact that angles on a straight line add up to 180 degrees) to find other relationships between them. There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

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## Solved Examples

If angle 1 measures 75 degrees, what is the measure of angle 2?

Since angle 1 and angle 2 are vertical angles, they are congruent. Therefore, angle 2 also measures 75 degrees.

If angle A is supplementary to angle B, and angle C is vertical to angle B, what is the measure of angle C?

Since angles B and C are vertical angles, they are congruent. Therefore, angle C is supplementary to angle A, and their sum is 180 degrees. So, if angle A measures x degrees, hen angle C measures 180 degrees minus x (180 ° – x).

If angle P is complementary to angle Q, and angle R is vertical to angle Q, what is the measure of angle R?

Since angles Q and R are vertical angles, they are congruent. Therefore, if angle P measures x degrees, then angle Q measures 90 – x degrees (since they are complementary), and angle R also measures 90 – x degrees (because they are congruent).

If angle X is vertical to angle Y, and angle Y is vertical to angle Z, what is the relationship between angles X and Z?

Since angles X and Y are vertical angles, they are congruent. Similarly, angles Y and Z are vertical angles and are also congruent. Therefore, angles X and Z are congruent by transitive property of equality.

In summary, to find the measure or relationship between vertical angles, we can use the fact that they are always congruent to each other. ## Vertical Angles FAQS

##### What is the difference between vertical angles and adjacent angles?

Vertical angles are formed when two lines intersect, and they are opposite angles that are across from each other. Adjacent angles, on the other hand, share a common side and vertex but do not overlap. In other words, adjacent angles are side-by-side, while vertical angles are across from each other.

##### How do you know if two angles are vertical angles?

Two angles are vertical angles if they are opposite angles that are across from each other and formed by the intersection of two lines. To identify vertical angles, look for pairs of angles that share a common vertex and are on opposite sides of the intersection of the two lines.

##### Can two angles be both vertical and adjacent?

No, two angles cannot be both vertical and adjacent. This is because vertical angles are opposite angles that are across from each other, while adjacent angles share a common side and vertex but do not overlap. Therefore, if two angles are adjacent, they cannot be vertical angles.

##### What is the measure of vertical angles when they are acute angles?

When vertical angles are acute angles (angles that measure less than 90 degrees), they are congruent and have the same measure as each other. This is true for all acute angles, regardless of their exact measure.

##### Can two obtuse angles be vertical angles?

Yes, two obtuse angles can be vertical angles. Vertical angles are formed by the intersection of two lines, so their angle measure does not depend on whether they are acute, right, or obtuse. As long as two angles are opposite angles that are across from each other and formed by the intersection of two lines, they are vertical angles and are congruent to each other. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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