Adjacent Angles Property: Relationship Between Acute and Obtuse Pairs

If two adjacent angles are not right angles, then one of them is obtuse and the other is acute.

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.