Question

logical reasoning what can you conclude about the labeled angles? 16. h ⊥ k

Explanation:

Step1: Recall perpendicular - line property

When two lines $h$ and $k$ are perpendicular ($h\perp k$), the angles formed at their intersection are right - angles.

Step2: Analyze the labeled angles

Since $h\perp k$, $\angle1+\angle2 = 90^{\circ}$ (complementary angles), $\angle1+\angle3=90^{\circ}$ (complementary angles), $\angle2$ and $\angle3$ are vertical angles so $\angle2=\angle3$, and $\angle1$ and $\angle2$ are adjacent and complementary, $\angle1$ and $\angle3$ are adjacent and complementary.

Answer:

$\angle1$ and $\angle2$ are complementary, $\angle1$ and $\angle3$ are complementary, $\angle2=\angle3$ (vertical angles)