Which one does not belong with the other three? Explain.

Four diagrams of angles. The first diagram shows a right angle split into angle 1 and angle 2 by a ray. The second diagram shows two separate angles: angle A which measures 50 degrees and angle B which measures 40 degrees. The third diagram shows a straight line split into angle 3 and angle 4 by a ray. The fourth diagram shows two separate angles: angle S which measures 65 degrees and angle T which measures 25 degrees.

Responses

first diagram;  It is the only diagram with adjacent angles.

second diagram;  It is the only diagram with complementary angles.

third diagram;  It is the only diagram with supplementary angles.

fourth diagram;  It is the only diagram with neither complementary nor supplementary angles.

The correct response is **second diagram; It is the only diagram with complementary angles**.

Here’s an explanation of each diagram:

1. **First diagram**: The right angle is split into two adjacent angles (angle 1 and angle 2), which are adjacent and also complementary since their sum is 90 degrees (right angle).
2. **Second diagram**: Angles A and B are complementary because their measures add up to 90 degrees (50 + 40 = 90 degrees).
3. **Third diagram**: A straight line forms supplementary angles (angle 3 and angle 4), as the angles sum to 180 degrees.
4. **Fourth diagram**: Angles S and T measure 65 and 25 degrees, respectively, and add up to 90 degrees (which is complementary), contradicting the provided statement saying they are neither complementary nor supplementary.

Thus, the **second diagram** stands out because it specifically focuses on two non-adjacent complementary angles, while the other diagrams deal with adjacent or supplementary angles.

Would you like further details or explanations?

Here are five related questions for further exploration:
1. What defines complementary angles versus supplementary angles?
2. Can adjacent angles always be complementary?
3. What are linear pairs, and how do they relate to supplementary angles?
4. How do complementary and supplementary angles apply to geometric shapes like triangles?
5. Can an angle be both complementary and supplementary under certain conditions?

**Tip**: Complementary angles always sum to 90 degrees, while supplementary angles sum to 180 degrees.

Which one does not belong with the other three? Explain.

Four diagrams of angles. The first diagram shows a right angle split into angle 1 and angle 2 by a ray. The second diagram shows two separate angles: angle A which measures 50 degrees and angle B which measures 40 degrees. The third diagram shows a straight line split into angle 3 and angle 4 by a ray. The fourth diagram shows two separate angles: angle S which measures 65 degrees and angle T which measures 25 degrees.

Explore how to identify which diagram does not belong by analyzing complementary and supplementary angles. Understand key concepts like adjacent angles, complementary angles, and supplementary angles. This problem is suitable for students in Grades 6-8.

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