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In angle vocabulary, what do we call two angles that share a common side and vertex but do not overlap?

  1. Vertical angles

  2. Adjacent angles

  3. Complementary angles

  4. Supplementary angles

The correct answer is: Adjacent angles

Two angles that share a common side and vertex but do not overlap are known as adjacent angles. This definition is key because adjacent angles are positioned next to each other and are formed when two lines meet at a point, creating angles that touch but remain distinct. The common side forms one edge of both angles, while the vertex is the point at which both angles originate. Understanding this concept is crucial in geometry, as it helps in analyzing relationships between angles in various figures. Vertical angles, on the other hand, are formed when two lines intersect, creating pairs of angles that are opposite each other, which does not fit the description provided in the question. Complementary angles refer to a pair of angles that add up to 90 degrees, while supplementary angles are those that sum to 180 degrees. Neither of these terms describes the relationship of sharing a common side and vertex without overlapping, which is why adjacent angles is the appropriate term in this context.