## Adjacent and Vertical Angles: Introduction

## FAQs on Difference Between Adjacent and Vertical Angles for JEE Main 2024

1. Do adjacent angles share a common vertex?

Yes, adjacent angles do share a common vertex. The vertex is the point where the two rays or line segments that form the angles meet. In the case of adjacent angles, they are positioned next to each other and have this common point of origin. This shared vertex is the starting point for both angles and represents the endpoint of one angle and the starting point of the other. The common vertex is a defining characteristic of adjacent angles, distinguishing them from other types of angles.

2. Can adjacent angles overlap?

No, adjacent angles do not overlap. By definition, adjacent angles are angles that share a common vertex and a common side but do not intersect or overlap with each other. They are positioned next to each other, with one angle on each side of the shared side. Overlapping would imply that the two angles occupy the same space or portion of the plane, which contradicts the concept of adjacent angles. It is important to distinguish adjacent angles from overlapping angles or intersecting angles, as adjacent angles have specific properties and relationships that are unique to their configuration.

3. Are vertical angles congruent?

Yes, vertical angles are congruent. Vertical angles are formed when two lines intersect, and they are located opposite each other. The key property of vertical angles is that they have equal measures. This means that if you measure one vertical angle, it will have the same measure as its corresponding vertical angle across the intersection. The congruence of vertical angles is a fundamental property in geometry and can be used to prove various theorems and solve geometric problems.

4. What is the sum of measures of adjacent angles?

The sum of measures of adjacent angles depends on the specific angles involved. Adjacent angles are angles that share a common vertex and a common side but do not overlap. When two adjacent angles are added together, their measures combine to form the measure of the larger angle that results from their combination. In other words, the sum of the measures of adjacent angles is equal to the measure of the larger angle formed by the two angles. This property holds true for any pair of adjacent angles, regardless of their individual measures or orientations.

5. Can adjacent angles be located on the same line?

Yes, adjacent angles can be located on the same line. When two angles share a common vertex and are on the same line, they are referred to as adjacent angles. In this case, the common side of the angles is the line itself. Adjacent angles on the same line can be found in various geometric configurations, such as intersecting lines, parallel lines, or in polygons. It is important to note that adjacent angles on the same line do not overlap or share any interior points; they are simply side by side.