Question

in the diagram shown, if (overline{tv}perpoverline{tw}), (mangle{tvw}=63^{circ}). does (overline{vw}) bisect (angle{tvx})? explain how you arrived at your conclusion.
in the diagram below, (overline{fh}perpoverline{fi}) and (overline{eg}). explain why (angle{efh}) and (angle{ifg}) must be complementary.

Explanation:

Step1: Recall perpendicular - angle property

If two lines are perpendicular, the angle between them is 90°. Since $\overline{FH}\perp\overline{FI}$, $\angle HFI = 90^{\circ}$.

Step2: Recall angle - addition postulate

$\angle EFI+\angle IFG=\angle EFG$. And $\angle EFG$ is a straight - angle, so $\angle EFG = 180^{\circ}$. Also, $\angle EFI+\angle IFG = 180^{\circ}$. Since $\angle HFI = 90^{\circ}$, and $\angle EFI+\angle IFG = 180^{\circ}$, we know that $\angle EFI$ and $\angle IFG$ are supplementary.

Answer:

$\angle EFI$ and $\angle IFG$ are supplementary because $\angle EFG$ is a straight - angle ($180^{\circ}$) and by the angle - addition postulate $\angle EFI+\angle IFG=\angle EFG$.