Question

1. in the diagram below, fi ⊥ fj and efg. explain why ∠efh and ∠hfg must be complementary

Explanation:

Step1: Recall perpendicular - angle property

Since $FH\perp FI$, $\angle HFI = 90^{\circ}$.

Step2: Analyze angle composition

$\angle EFG$ is a straight - angle, so $\angle EFG=180^{\circ}$. And $\angle EFG=\angle EFH+\angle HFI+\angle IFG$.

Step3: Substitute values and simplify

Substituting $\angle HFI = 90^{\circ}$ into $\angle EFG=\angle EFH+\angle HFI+\angle IFG$, we get $180^{\circ}=\angle EFH + 90^{\circ}+\angle IFG$. Then, subtracting $90^{\circ}$ from both sides gives $\angle EFH+\angle IFG = 90^{\circ}$.

Answer:

Since the sum of $\angle EFH$ and $\angle IFG$ is $90^{\circ}$, they are complementary by the definition of complementary angles.