Math Problem Statement

Determine whether the angles are complementary, supplementary,or neither

Determine whether the angles are complementary, supplementary, or neither.

Solution

To determine whether the given angles are complementary, supplementary, or neither, let's evaluate their properties:

  • Complementary angles are two angles whose sum is 9090^\circ.
  • Supplementary angles are two angles whose sum is 180180^\circ.
  • If the sum is neither 9090^\circ nor 180180^\circ, the angles are neither complementary nor supplementary.

In the image, the angles provided are:

  • 148148^\circ
  • 3232^\circ

Now, let's calculate their sum: 148+32=180148^\circ + 32^\circ = 180^\circ

Since the sum is exactly 180180^\circ, these two angles are supplementary.

Would you like more details or have any questions? Here are five related questions to expand on this:

  1. What are some examples of complementary angles in real life?
  2. Can two obtuse angles be supplementary?
  3. What is the difference between adjacent and non-adjacent supplementary angles?
  4. How can we identify angles formed by intersecting lines?
  5. Can angles be supplementary if they are not adjacent?

Tip: Remember, supplementary angles can be adjacent or non-adjacent; their sum is what matters!

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Math Problem Analysis

Mathematical Concepts

Geometry
Angle Relationships

Formulas

Sum of angles: Complementary (sum = 90°), Supplementary (sum = 180°)

Theorems

Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8