Adjacent Angles Property: Can Two Obtuse Angles Share a Side?

To determine if two adjacent angles can both be obtuse, we first need to recall the definition of an obtuse angle and what it means for angles to be adjacent.

• An obtuse angle measures more than $90^\circ$ but less than $180^\circ$.
• Adjacent angles are two angles that share a common side and vertex.
• When we consider adjacent angles that form a linear pair, their sum must equal $180^\circ$.

For two angles to both be obtuse, each must measure more than $90^\circ$. Let's consider two angles, $a$ and $b$, that are adjacent and both obtuse:

• $a > 90^\circ$
• $b > 90^\circ$

Adding both inequalities gives:

$a + b > 180^\circ$

This sum $a + b$ would contradict the requirement that adjacent angles forming a linear pair sum to exactly $180^\circ$.

Therefore, two adjacent angles cannot both be obtuse, as their sums would exceed the allowable amount for a linear pair.

Thus, it is not possible for two adjacent angles to be obtuse. The correct answer is False.