Subjects geometry

Adjacent Angles 9B9Be5

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1. **State the problem:** A student claims that the sum of the measures of a pair of adjacent angles must equal 180°. 2. **Recall definitions:** Adjacent angles share a common vertex and a common side but do not necessarily sum to 180°. 3. **Important rule:** When two adjacent angles form a straight line, they are called a linear pair, and their measures sum to 180°. 4. **Evaluate the student's claim:** The student says the sum must be 180°, but this is only true if the adjacent angles form a linear pair (i.e., lie on a straight line). 5. **Conclusion:** Adjacent angles do not always sum to 180°; they only do so if they form a linear pair. **Correct answer:** D) The student is not correct; a pair of adjacent angles must share a common vertex, share a common side, and not overlap. They may equal 180° but do not have to.
Angle 1Angle 2Straight line