Question

in the diagram, are \\(\overleftrightarrow{ac}\\) and \\(\overleftrightarrow{df}\\) parallel? explai\

1. \

(the diagram shows two horizontal lines ac and df with a transversal intersecting them, creating a 143° angle at b on ac and a 37° angle at e on df.)

Explanation:

Step1: Find supplementary angle of 143°

Calculate the angle adjacent to $143^\circ$ on line $\overleftrightarrow{AC}$:
$180^\circ - 143^\circ = 37^\circ$

Step2: Compare angles to test parallelism

The calculated $37^\circ$ angle is equal to the given $37^\circ$ angle on line $\overleftrightarrow{DF}$. These are corresponding angles, and congruent corresponding angles confirm parallel lines.

Answer:

Yes, $\overleftrightarrow{AC}$ and $\overleftrightarrow{DF}$ are parallel. The supplementary angle of $143^\circ$ is $37^\circ$, which matches the given $37^\circ$ angle, forming congruent corresponding angles, a sufficient condition for parallel lines.