Question

1. in the diagram, are $overleftrightarrow{ac}$ and $overleftrightarrow{df}$ parallel? explain your reasoning. (see example 2.)

23)

Explanation:

Step1: Solve for adjacent angle (22)

Calculate supplementary angle:
$180^\circ - 143^\circ = 37^\circ$

Step2: Compare angles (22)

The calculated angle equals $37^\circ$, so corresponding angles are congruent.

Step3: Analyze angle relationship (23)

The two $62^\circ$ angles are alternate interior angles, which are congruent.

Answer:

1. $\overleftrightarrow{AC}$ and $\overleftrightarrow{DF}$ are parallel. The supplementary angle of $143^\circ$ is $37^\circ$, which matches the given angle, proving corresponding angles are congruent (a parallel line criterion).
2. $\overleftrightarrow{AC}$ and $\overleftrightarrow{DF}$ are parallel. The two $62^\circ$ angles are congruent alternate interior angles, which satisfies a parallel line criterion.