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

Adjacent Angles with Linear Pair Formation

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

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Step-by-step written solution

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1

Understand the problem

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

2

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.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Adjacent angles share a vertex and side without overlapping
  • Technique: Add two right angles: 90°+90°=180°90° + 90° = 180°
  • Check: Two adjacent right angles form a straight line totaling 180° ✓

Common Mistakes

Avoid these frequent errors
  • Thinking adjacent angles cannot both be right angles
    Don't assume adjacent right angles are impossible because they seem "too big"! This ignores that 90° + 90° = 180° forms a straight line. Always remember that adjacent angles can have any measures as long as they share a vertex and side.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

What exactly does 'adjacent' mean for angles?

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Adjacent angles are like puzzle pieces that fit together! They share a common vertex (corner point) and a common side, but they don't overlap or have any gap between them.

If two right angles are adjacent, what shape do they make?

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Two adjacent right angles create a straight line! Since each right angle is 90°, together they measure 90°+90°=180°90° + 90° = 180°, which is exactly a straight angle.

Can three right angles be adjacent to each other?

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No! Three right angles would total 90°+90°+90°=270°90° + 90° + 90° = 270°. Since angles around a point only go up to 360°, you'd need a fourth 90° angle to complete the circle.

Are adjacent right angles the same as perpendicular lines?

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Not exactly! Perpendicular lines form four right angles at their intersection. Adjacent right angles are just two of those four angles that happen to be next to each other.

How can I visualize this better?

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Think of opening a book! When the book is completely flat, the two pages form adjacent right angles with the spine. Each page makes a 90° angle with the table, totaling 180°.

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