Math Problem Statement

Which angles are adjacent angles in the given diagram?

Solution

To determine which angles are adjacent, let's first define adjacent angles:

Adjacent angles are two angles that share a common side and a common vertex but do not overlap.

In this diagram:

  • GHJ\angle GHJ is formed by lines GJGJ and HJHJ.
  • We need to find an angle that shares a common side with GHJ\angle GHJ.

Let's analyze each option:

  1. GHJ\angle GHJ and FEC\angle FEC:

    • These angles do not share a common side or vertex, so they are not adjacent.
  2. GHJ\angle GHJ and DEC\angle DEC:

    • These angles also do not share a common side or vertex, so they are not adjacent.
  3. GHJ\angle GHJ and GHE\angle GHE:

    • These two angles share the common vertex HH and the common side GHGH. Thus, they are adjacent angles.
  4. GHJ\angle GHJ and IHE\angle IHE:

    • These angles do not share a common side or vertex, so they are not adjacent.

The correct answer is: GHJ\angle GHJ and GHE\angle GHE.

Would you like further clarification on this or related concepts?

Here are 5 related questions for further exploration:

  1. What is the difference between adjacent and supplementary angles?
  2. How do we determine vertical angles from a diagram like this?
  3. Can adjacent angles also be complementary?
  4. How do you calculate the measure of adjacent angles when one angle's measure is given?
  5. What are alternate interior angles, and how do they relate to adjacent angles?

Tip: Adjacent angles always share a side and a vertex, but they don't overlap!

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Math Problem Analysis

Mathematical Concepts

Geometry
Adjacent Angles
Angle Properties

Formulas

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Theorems

Adjacent Angles Theorem

Suitable Grade Level

Grades 6-8