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101 LearnersLast updated on September 3, 2025
Properties of Adjacent Angles
Adjacent angles are a fundamental concept in geometry that possess unique properties. Understanding these properties helps students solve various geometric problems involving angles. Adjacent angles are angles that have a common side and a common vertex but do not overlap. Exploring the properties of adjacent angles aids in analyzing and solving problems related to angle measures, linear pairs, and angle sum properties. Now, let us learn more about the properties of adjacent angles.
What are the Properties of Adjacent Angles?
The properties of adjacent angles are straightforward and help students understand relationships between angles. These properties are derived from basic geometric principles. Some of the key properties of adjacent angles include:
Property 1: Common Vertex and Side Adjacent angles share a common vertex and a common side.
Property 2: Sum of Angles: The sum of adjacent angles in a linear pair is 180 degrees.
Property 3: Non-overlapping Adjacent angles do not overlap each other.
Property 4: Angle Addition Postulate: If a point is in the interior of an angle, the sum of the two adjacent angles formed equals the measure of the original angle.
Property 5: Complementary and Supplementary Relationships: Adjacent angles can form complementary or supplementary pairs based on their sum being 90 or 180 degrees respectively.
Tips and Tricks for Properties of Adjacent Angles
Students can often mix up different angle properties. To avoid confusion, keep these tips and tricks in mind:
Common Vertex and Side: Remember that adjacent angles always share a common vertex and side. Draw diagrams to better visualize this relationship.
Linear Pair Sum: Adjacent angles forming a linear pair will always add up to 180 degrees. Use this property to solve related problems.
Clear Understanding of Overlapping: Ensure that students know adjacent angles do not overlap each other.
Confusing Adjacent Angles with Vertical Angles
Students should remember that adjacent angles share a common side and vertex, while vertical angles are opposite each other and share a vertex but not a side.
Mistake 1
Misinterpreting Linear Pair Relationships
Students should remember that if two adjacent angles form a linear pair, their sum is 180 degrees.
Mistake 2
Overlapping Angles Misconception
Adjacent angles do not overlap. Students should ensure diagrams clearly show non-overlapping angles to avoid confusion.
Mistake 3
Misunderstanding Angle Addition
Students should use the angle addition postulate correctly: if a point lies in the interior of an angle, the adjacent angles formed add up to the measure of the original angle.
Mistake 4
Ignoring Complementary and Supplementary Concepts
Students should remember that adjacent angles can be complementary or supplementary if their measures add up to 90 degrees or 180 degrees, respectively.
Mistake 5
Solved Examples on the Properties of Adjacent Angles
In a diagram, angles AOB and BOC are adjacent, and angle AOB is 70 degrees. What is the measure of angle BOC if they form a linear pair?
BOC = 110 degrees.
Problem 1
Since AOB and BOC form a linear pair, their sum is 180 degrees. Thus, BOC = 180 - 70 = 110 degrees.
Two adjacent angles, XYZ and ZYW, are complementary. If angle XYZ is 35 degrees, what is the measure of angle ZYW?
Explanation
ZYW = 55 degrees.
Problem 2
Since XYZ and ZYW are complementary, their sum is 90 degrees. Thus, ZYW = 90 - 35 = 55 degrees.
In a picture, angles PQR and QRS are adjacent. If angle PQR = 45 degrees and angle QRS = 45 degrees, what is the relationship between these angles?
Explanation
PQR and QRS are complementary angles.
Problem 3
Since PQR and QRS sum up to 90 degrees, they are complementary angles.
If angle ABC is divided into two adjacent angles, ABD and DBC, with angle ABD measuring 30 degrees and the whole angle ABC measuring 75 degrees, what is the measure of angle DBC?
Explanation
DBC = 45 degrees.
Problem 4
According to the angle addition postulate, ABD + DBC = ABC. So, DBC = 75 - 30 = 45 degrees.
Angles LMN and MNO are adjacent and form a linear pair. If angle LMN is 120 degrees, what is the measure of angle MNO?
Explanation
MNO = 60 degrees.
Adjacent angles are angles with a common side and a common vertex that do not overlap.
1.What is a linear pair of angles?
2.Can adjacent angles be complementary?
3.How do adjacent angles relate to the angle addition postulate?
4.Are vertical angles the same as adjacent angles?
Common Mistakes and How to Avoid Them in Properties of Adjacent Angles
Students often make mistakes when dealing with adjacent angles. Here are some common errors and how to avoid them.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
