Can Two Right Angles Form a Linear Pair?

In geometry, a linear pair is a pair of adjacent angles formed when two lines intersect. The sum of the angles in a linear pair always adds up to 180°. A common question that arises is whether two right angles can form a linear pair.

To answer this, let’s break down the concepts of right angles and linear pairs, and explore whether they can coexist.

1. Understanding Right Angles

A right angle is an angle that measures exactly 90°. Right angles are typically formed when two lines are perpendicular to each other. In geometric terms, a right angle is represented by a square symbol in the corner of the angle.

2. Understanding a Linear Pair

A linear pair is a pair of adjacent angles that are formed by two intersecting lines. These angles are adjacent, meaning they share a common side, and the non-common sides of the two angles form a straight line. The key property of a linear pair is that the sum of the two angles in the pair is always 180°.

Mathematically: Angle 1+Angle 2=180∘\text{Angle 1} + \text{Angle 2} = 180^\circ

Example of a Linear Pair:

If one angle is 90° and the other is 90°, their sum will be: 90∘+90∘=180∘90^\circ + 90^\circ = 180^\circ

This is a valid linear pair, as the sum equals 180°, which is the defining characteristic of a linear pair.

3. Can Two Right Angles Form a Linear Pair?

Yes, two right angles can form a linear pair. This happens when two lines intersect in such a way that they form two adjacent right angles. Since each right angle measures 90°, the sum of the two angles will be: 90∘+90∘=180∘90^\circ + 90^\circ = 180^\circ

This satisfies the definition of a linear pair, as the sum of the angles is 180°, and the two angles are adjacent (sharing a common side).

Example of Two Right Angles Forming a Linear Pair:

Imagine two perpendicular lines intersecting at a point. The angles formed at the intersection are both right angles. These two right angles are adjacent and share a common side. Therefore, they form a linear pair.

4. Conclusion

Yes, two right angles can form a linear pair. The sum of the two right angles is 180°, which satisfies the definition of a linear pair. Therefore, two right angles can indeed form a linear pair when they are adjacent and formed by two intersecting lines.

Also Check:

• Can Two Obtuse Angles Be Adjacent

• Can Two Acute Angles Form a Linear Pair

• How Many Right Angles Can a Triangle Have

• Can Two Adjacent Angles Be Complementary? Understanding and Illustrating the Concept