Adjacent Angle Identification: Analyzing Intersecting Line Segments

Adjacent Angles with Intersecting Lines

Does the diagram show an adjacent angle?

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Step-by-step video solution

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00:00 Is there an adjacent angle in the drawing?
00:02 An adjacent angle complements an angle to form a straight angle on a line
00:05 It appears that in our drawing there are no adjacent angles

Step-by-step written solution

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1

Understand the problem

Does the diagram show an adjacent angle?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Inspect the given diagram for angles.
  • Step 2: Determine if any angles share a common vertex and a common side.
  • Step 3: Verify that the angles do not overlap.

Now, let's work through each step:

Step 1: Inspecting the diagram, we notice several intersecting lines.

Step 2: To check for adjacent angles, we look for pairs of angles that share both a common vertex and a common side. An adjacent angle must be formed by such pairs, ensuring they do not overlap.

Step 3: Based on our definition, after closely examining the diagram, no pair of angles in the diagram seems to satisfy the definition of adjacent angles. The intersecting lines form angles that don't share a common arm with any other angle at the same vertex in the manner required for adjacency.

Therefore, the solution to the problem is No, the diagram does not show an adjacent angle.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Definition: Adjacent angles share a vertex and common side without overlapping
  • Technique: Look for angles at same vertex with one shared ray
  • Check: Verify angles touch but don't overlap at their common boundary ✓

Common Mistakes

Avoid these frequent errors
  • Confusing any angles at same vertex as adjacent
    Don't assume all angles at one vertex are adjacent = wrong identification! Angles must share exactly one common side (ray) between them. Always check that the angles have a shared boundary ray, not just the same vertex point.

Practice Quiz

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Does the drawing show an adjacent angle?

FAQ

Everything you need to know about this question

What exactly makes two angles adjacent?

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Two angles are adjacent when they meet three requirements: they share a common vertex, they share a common side (ray), and they don't overlap. Think of it like two puzzle pieces that fit perfectly next to each other!

Can angles be adjacent if they're formed by different intersecting lines?

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Yes! Adjacent angles can be formed by any intersecting lines or rays. What matters is that the two angles share a vertex and one common ray, regardless of how many lines create the intersection.

How do I identify the common side between two angles?

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Look for the ray that forms the boundary between the two angles. This ray should be part of both angles - it's where one angle ends and the other begins.

What if I see angles that share a vertex but don't touch?

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Those are not adjacent! Adjacent angles must actually touch along their common side. If there's a gap between them or another angle in between, they're not adjacent.

Why doesn't this diagram show adjacent angles?

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Looking at the intersecting lines in this diagram, while there are multiple angles formed at intersection points, none of the angle pairs share a common ray in the way required for adjacency. The angles either overlap or don't share the right boundary.

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