Subjects geometry

Adjacent Angles B58E04

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1. The problem asks which pairs of angles can be adjacent angles. 2. Adjacent angles share a common side and vertex, and their measures add up to less than or equal to 180° because they form a straight line or part of it. 3. We check each pair by adding their measures: A) $42^\circ + 48^\circ = 90^\circ$ which is less than 180°, so they can be adjacent. B) Same as A, so they can be adjacent. C) $105^\circ + 73^\circ = 178^\circ$ which is less than 180°, so they can be adjacent. D) $95^\circ + 80^\circ = 175^\circ$ which is less than 180°, so they can be adjacent. 4. However, the problem states "acute angles" which means angles less than 90°. 5. Check which angles are acute: - 42° and 48° are acute. - 105° is not acute. - 73° is acute. - 95° is not acute. - 80° is acute. 6. So only pairs with both angles acute can be adjacent acute angles. 7. Therefore, only pair A (42° and 48°) consists of two acute angles and can be adjacent. Final answer: A) A 42° angle and a 48° angle can be adjacent angles.