Adjacent Angles - TutorOne USA

Adjacent Angles

Chapter 34

Adjacent Angles Concept Explanation:

Adjacent angles are two angles that have a common side and a common vertex but do not overlap. They are found next to each other in geometric figures.

For example, in the diagram below, $\angle AOB$ and $\angle BOC$ are adjacent angles:

Common Mistakes:

Misidentifying Adjacent Angles: Students sometimes confuse adjacent angles with angles that share only a vertex or a side.
Overlapping Angles: Ensure that adjacent angles do not overlap.

Helpful Tips:

Visualize Using a Diagram: Draw out the angles to ensure they are adjacent.
Check for Shared Side and Vertex: Always confirm that both angles share exactly one side and one vertex.

Hard Questions:

Q1: If $\angle AOB = 40^\circ$ and $\angle BOC = 50^\circ$ , what is $\angle AOC$ ?

Step-by-Step Solution:

Since $\angle AOB$ and $\angle BOC$ are adjacent, their sum gives $\angle AOC$ :

$\angle AOC = \angle AOB + \angle BOC = 40^\circ + 50^\circ = 90^\circ$

Answer:

The result is $90^\circ$ .

Q2: If $\angle XOY = 70^\circ$ and $\angle YOZ = 30^\circ$ , what is $\angle XOZ$ ?

Step-by-Step Solution:

Since $\angle XOY$ and $\angle YOZ$ are adjacent, their sum gives $\angle XOZ$ :

$\angle XOZ = \angle XOY + \angle YOZ = 70^\circ + 30^\circ = 100^\circ$

Answer:

The result is $100^\circ$ .

Q3: Two adjacent angles sum to $120^\circ$ . If one angle measures $75^\circ$ , find the other angle.

Step-by-Step Solution:

Let the unknown angle be $x$ :

$75^\circ + x = 120^\circ$

$x = 120^\circ - 75^\circ = 45^\circ$

Answer:

The other angle is $45^\circ$

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