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If the sum of two adjacent angles is 180...

If the sum of two adjacent angles is `180^@`, then the ___ arms of the two angles are opposite rays.

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To solve the question, we need to understand the relationship between adjacent angles and their arms when their sum is 180 degrees. ### Step-by-Step Solution: 1. **Understanding Adjacent Angles**: - Adjacent angles are two angles that share a common vertex and a common arm but do not overlap. 2. **Given Condition**: - The problem states that the sum of the two adjacent angles is 180 degrees. This means that together, they form a straight angle. 3. **Visualizing the Angles**: - If we visualize two adjacent angles, let’s denote them as ∠AOB and ∠BOC, where O is the common vertex, and OB is the common arm. - Since the sum of these angles is 180 degrees, we can say that the angles together form a straight line. 4. **Identifying the Arms**: - The arms of the angles are OA (for ∠AOB) and OC (for ∠BOC). - The common arm is OB, while OA and OC are the non-common arms. 5. **Understanding Opposite Rays**: - Opposite rays are two rays that share a common endpoint and extend in opposite directions. - In this case, OA and OC extend in opposite directions from point O. 6. **Conclusion**: - Therefore, the non-common arms of the two angles (OA and OC) are opposite rays. ### Final Answer: The non-common arms of the two angles are opposite rays. ---
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