Adjacent Right Angles: Analyzing 90-Degree Angle Pairs in Geometry

Question

Is it possible to have two adjacent angles that are both right angles?

Step-by-Step Solution

To solve this problem, we'll consider the definition and properties of right and adjacent angles.

  • Step 1: Definition of Adjacent Angles
    Adjacent angles share a common vertex and a common side, but do not overlap. They are typically formed when two lines intersect.
  • Step 2: Characteristics of Right Angles
    A right angle measures 9090^\circ. If two such angles are placed adjacent to each other, their total is 90+90=18090^\circ + 90^\circ = 180^\circ.
  • Step 3: Geometric Interpretation
    Two right angles, each 9090^\circ, can indeed share a common side, forming a straight line (also known as a linear pair). This illustrates that it is possible to have two adjacent right angles.

When visualized, these two right angles can be seen as forming a straight angle or line. This conclusion can be confirmed by considering the total degrees along a straight line: 180180^\circ.

Therefore, it is indeed possible for two adjacent angles to both be right angles. These right angles together will form a straight line.

Therefore, the solution to the problem is Yes.

Answer

Yes