Question
6. Complementary angles are adjacent. 37. Angles in a linear pair are supplements of each other.
Ask by Davey Nichols. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Complementary angles do not have to be adjacent, but angles in a linear pair are always supplementary.
Solution
Let's evaluate each of the statements you've provided:
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**6. Complementary angles are adjacent.**
**Evaluation:** **False**
**Explanation:**
- **Complementary Angles:** Two angles whose measures add up to **90 degrees**.
- **Adjacent Angles:** Two angles that share a common vertex and a common side but do not overlap.
While complementary angles **can be** adjacent (for example, two angles that form a right angle together), it is **not a requirement** for them to be adjacent. Complementary angles can exist separately and do not need to share a common side or vertex. Therefore, the statement that "complementary angles are adjacent" is **not always true**.
**Example:**
- Consider one angle measuring 30 degrees and another measuring 60 degrees. These angles are complementary because \(30° + 60° = 90°\). However, they don't have to be next to each other; they can be located in different parts of a diagram without sharing a common side.
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**37. Angles in a linear pair are supplements of each other.**
**Evaluation:** **True**
**Explanation:**
- **Linear Pair:** A pair of adjacent angles formed when two lines intersect. The non-common sides of the angles form a straight line.
- **Supplementary Angles:** Two angles whose measures add up to **180 degrees**.
By definition, angles in a linear pair are supplementary because the straight line they form inherently measures 180 degrees. Since the two angles are adjacent and their non-common sides lie on this straight line, their measures must sum to 180 degrees.
**Example:**
- If two angles form a linear pair and one angle measures 110 degrees, the other must measure \(180° - 110° = 70°\) to satisfy the supplementary condition.
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**Summary:**
- **Statement 6:** *False* — Complementary angles do not have to be adjacent.
- **Statement 37:** *True* — Angles in a linear pair are indeed supplementary.
If you have more statements or need further clarification on these concepts, feel free to ask!
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
While complementary angles sum up to 90 degrees, they are not necessarily adjacent; they can be separate angles as well! Picture two angles like friends splitting a pizza: they might not be sitting next to each other but still share the same tasty slice of 90 degrees! Similarly, angles in a linear pair definitely sum up to 180 degrees and are always adjacent, meaning they sit side by side, sharing a vertex and a common side. Think of it this way: if two angles form a straight line together, they're essentially best buddies completing a full turn together!
