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

It is possible for two adjacent angles to be obtuse.

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.