Adjacent Angles Practice Problems and Worksheets | Step-by-Step

Master adjacent angles with guided practice problems. Learn to identify, calculate, and solve adjacent angle relationships in parallel lines and intersecting lines.

📚What You'll Master in Adjacent Angles Practice
  • Identify adjacent angles formed when two straight lines intersect
  • Apply the supplementary property: adjacent angles always sum to 180°
  • Distinguish between adjacent, corresponding, alternate, and opposite angles
  • Solve for unknown angles using adjacent angle relationships
  • Work with adjacent angles in parallel lines and transversal problems
  • Calculate missing angles in triangles using adjacent angle properties

Understanding Adjacent angles

Complete explanation with examples

What does adjacent angle mean?

Adjacent angles are the pair of angles formed when two lines intersect each other. These angles are formed at the point where the intersection occurs, and are adjacent to eachother - hence its name. Another pair of angles that are formed at the intersection of two straight lines are the opposite angles, but this pair of angles are opposite at the vertex and not adjacent, so we should not confuse them with adjacent angles. Adjacent angles are always supplementary, that is, together they equal 180° 180° .

The following illustration shows two examples of what adjacent angles look like. One example is red and the other blue.

Adjacent angles new

Detailed explanation

Practice Adjacent angles

Test your knowledge with 48 quizzes

Which type of angles are shown in the figure below?

Examples with solutions for Adjacent angles

Step-by-step solutions included
Exercise #1

Does the diagram show an adjacent angle?

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.

Answer:

No

Video Solution
Exercise #2

Is it possible to have two adjacent angles, one of which is obtuse and the other right?

Step-by-Step Solution

Remember the definition of adjacent angles:

Adjacent angles always complement each other up to one hundred eighty degrees, that is, their sum is 180 degrees.

This situation is impossible since a right angle equals 90 degrees, an obtuse angle is greater than 90 degrees.

Therefore, together their sum will be greater than 180 degrees.

Answer:

No

Video Solution
Exercise #3

Does the diagram show an adjacent angle?

Step-by-Step Solution

To determine whether the diagram shows adjacent angles, we need to confirm the presence of two properties:
1. Two angles must share a common vertex.
2. These angles must have a common arm and should not overlap.

Based on the given representation, the provided diagram consists solely of a single line. There are no visible intersecting lines or vertices from which angles can originate. Without intersection, there cannot be distinct angles, and thereby no adjacent angles can be identified.

Therefore, the diagram lacks the necessary properties to demonstrate adjacent angles. Hence, the correct choice is No.

Answer:

No

Video Solution
Exercise #4

Does the drawing show an adjacent angle?

Step-by-Step Solution

Adjacent angles are angles whose sum together is 180 degrees.

In the attached drawing, it is evident that there is no angle of 180 degrees, and no pair of angles can create such a situation.

Therefore, in the drawing there are no adjacent angles.

Answer:

Not true

Video Solution
Exercise #5

Does the drawing show an adjacent angle?

Step-by-Step Solution

Adjacent angles are angles whose sum together is 180 degrees.

In the attached drawing, it is evident that there is no angle of 180 degrees, and no pair of angles can create such a situation.

Therefore, in the drawing there are no adjacent angles.

Answer:

Not true

Video Solution

Frequently Asked Questions

Everything you need to know about Adjacent angles

What are adjacent angles and how do I identify them?

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Adjacent angles are pairs of angles formed when two straight lines intersect at a point. They share a common vertex and are next to each other (adjacent). The key property is that adjacent angles are always supplementary, meaning they add up to exactly 180°.

How do I solve adjacent angle problems step by step?

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Follow these steps: 1) Identify the adjacent angle pair at the intersection point, 2) Set up the equation knowing they sum to 180°, 3) Substitute known angle measures, 4) Solve for the unknown angle by subtracting the known angle from 180°.

What's the difference between adjacent angles and corresponding angles?

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Adjacent angles form at the same intersection point and are supplementary (sum to 180°). Corresponding angles occur when parallel lines are cut by a transversal, are in matching positions, and are equal to each other, not supplementary.

Can two obtuse angles be adjacent to each other?

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No, two obtuse angles cannot be adjacent. Since obtuse angles are greater than 90°, two of them would sum to more than 180°. Adjacent angles must be supplementary (sum to exactly 180°), so at least one must be acute.

How do adjacent angles help solve triangle problems?

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Adjacent angles are useful when triangle sides are extended to show exterior angles. The exterior angle and its corresponding interior angle are adjacent and supplementary. This relationship helps find missing interior angles when combined with the triangle angle sum property (180°).

What are the most common mistakes with adjacent angles?

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Common errors include: confusing adjacent with opposite angles (which are equal, not supplementary), forgetting that adjacent angles must sum to 180°, and misidentifying angle pairs in parallel line diagrams. Always check that angles share a vertex and are next to each other.

How do I work with adjacent angles in parallel line problems?

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In parallel line problems, first identify if you're dealing with adjacent angles (at intersection points) or other angle relationships like corresponding or alternate angles. Adjacent angles will always be supplementary regardless of whether the lines are parallel.

What formulas do I need for adjacent angle calculations?

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The main formula is: Adjacent Angle 1 + Adjacent Angle 2 = 180°. If one angle measures x°, then its adjacent angle measures (180 - x)°. This supplementary relationship is the foundation for all adjacent angle problems.

More Adjacent angles Questions

Click on any question to see the complete solution with step-by-step explanations

Angles in Parallel Lines

Adjacent Angle Identification: Analyzing Line Intersection Diagram Adjacent Angles: Analyzing Intersecting Lines in Geometric Diagram Adjacent Angle Identification: Analyzing Geometric Line Intersections Geometry Problem: Identifying Adjacent Angle Relationships Adjacent Angles: Identifying Geometric Properties in Line Intersections

Continue Your Math Journey

Master Adjacent angles first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

Parallel lines

Topics Learned in Later Sections

Angles In Parallel LinesAlternate anglesCorresponding anglesCollateral anglesVertically Opposite AnglesCorresponding exterior anglesAlternate interior anglesPerpendicular Lines

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