Assertion reason question statement i assertion the sum of the measure...
Assertion: The Sum of Angles in a Linear Pair is 180 Degrees
The assertion states that when two angles form a linear pair, their measures always add up to 180 degrees. This is a fundamental property of angles formed by intersecting lines.
Key Points:
- Linear pairs consist of two adjacent angles that share a common vertex and a side.
- When two lines intersect, they create four angles. Each pair of adjacent angles is a linear pair.
- Since they lie on a straight line, the angles in a linear pair must add up to form a straight angle, which measures 180 degrees.
Reason: Formation of Linear Pairs by Intersecting Lines
The reason explains that when two lines intersect at a single point, they create linear pairs of angles.
Key Points:
- The intersection of two lines produces four angles.
- Each angle formed at the intersection is adjacent to another angle, resulting in two linear pairs.
- For example, if angle A and angle B form a linear pair, then angle A + angle B = 180 degrees.
Conclusion:
Both the assertion and reason are correct and related. The sum of the measures of angles in a linear pair is indeed 180 degrees, and this occurs due to the nature of intersecting lines. Understanding these concepts is crucial in geometry, particularly in solving problems involving angles.