Angles with parallel lines

Question 1

Two parallel streets, Oak Street and Pine Street, are crossed by Maple Avenue. The interior angle formed between Oak Street and Maple Avenue on the left side of the avenue is labeled ∠M, and the interior angle formed between Pine Street and Maple Avenue on the right side of the avenue is labeled ∠N. Which statement correctly explains why ∠M and ∠N are equal?

Accepted Answer

Because we can slide (translate) angle ∠M along Maple Avenue until it coincides with angle ∠N; the translation does not change the angle’s size, and the sides line up only because the streets are parallel.

Answer

Because ∠M and ∠N are vertical angles, and all vertical angles are equal.

Answer

Because the two interior angles on a straight line must add up to 180°, so ∠M + ∠N = 180°, making them equal.

Answer

Because parallel streets are the same distance apart, so any angles they make with a crossing road must be the same.

Question 2

Lines AB and CD are parallel and are cut by transversal EF. At the intersection with AB the angles are numbered 1 (top‑left), 2 (top‑right), 3 (bottom‑left), 4 (bottom‑right). At the intersection with CD the angles are numbered 5 (top‑left), 6 (top‑right), 7 (bottom‑left), 8 (bottom‑right). Which pair of angles are alternate interior angles?

Accepted Answer

Angles 3 and 6

Answer

Angles 2 and 5

Answer

Angles 7 and 8

Answer

Angles 1 and 4

Question 3

In a park design, two straight walkways are drawn parallel to each other and a third walkway cuts across them, creating the marked angles ∠X and ∠Y as alternate interior angles. Which statement correctly explains why ∠X and ∠Y have the same measure?

Accepted Answer

A translation that slides the whole figure along the transversal moves ∠X exactly onto ∠Y, and a translation does not change angle size.

Answer

All angles around a point total 360°, so each of these angles must be 180°.

Answer

∠X and ∠Y lie on a straight line, so together they must add to 180°, making them equal.

Answer

∠X and ∠Y are opposite each other at the intersection, so they are vertical angles and therefore equal.

Try three questions

In a park design, two straight walkways are drawn parallel to each other and a third walkway cuts across them, creating the marked angles ∠X and ∠Y as alternate interior angles. Which statement correctly explains why ∠X and ∠Y have the same measure?

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