Parallelism Math Example 2

Follow the full solution, then compare it with the other examples linked below.

medium

Transversal

t

crosses parallel lines

\ell_1 \parallel \ell_2

. If the co-interior (same-side interior) angle at

\ell_1

65°

, find the co-interior angle at

\ell_2

and the alternate interior angle at

\ell_2

1
Step 1: Co-interior angles between parallel lines are supplementary: $65° + \angle_2 = 180°$ , so $\angle_2 = 115°$ .
2
Step 2: The alternate interior angle at $\ell_2$ is on the opposite side of the transversal from $\angle_2$ . Alternate interior angles are equal when lines are parallel: alternate interior angle $= 65°$ .
3
Step 3: Verify: $65° + 115° = 180°$ ✓

Answer

Co-interior angle at

\ell_2 = 115°

; alternate interior angle at

\ell_2 = 65°

Parallel lines cut by a transversal produce co-interior angles that sum to

180°

and alternate interior angles that are equal. These are standard tests and consequences of parallelism.

About Parallelism

Lines in the same plane that never intersect because they maintain a constant distance from each other.

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