Adjacent Angles Property: Relationship Between Acute and Obtuse Pairs

To solve the problem, let’s consider the nature of adjacent angles:

• Step 1: Adjacent angles are two angles that share a common side and vertex. If two adjacent angles form a straight line, their measures sum up to $180^\circ$.
• Step 2: According to the problem, neither angle is a right angle, meaning neither is $90^\circ$.
• Step 3: Given this constraint, analyze the possibilities:
• If one angle is acute (less than $90^\circ$), then the other must be more than $90^\circ$ to make the total $180^\circ$. Therefore, the other angle is obtuse.
• If one angle is obtuse (greater than $90^\circ$), then the other must be less than $90^\circ$ to make the total $180^\circ$. Thus, the other angle is acute.

Since both scenarios involve one angle being acute and the other obtuse, we verify that the statement is correct.

Therefore, the statement is true.