volume_mute

Refer to the figure. Identify

publish date: 2023/09/19 22:46:00 GMT+10

volume_mute
  1. Two corresponding angles (1) transparent
  2. One interior angle (2) transparent
  3. A pair of alternate interior angles (3) transparent

Please drag and drop the selected option in the right place or type it instead
∠1 and ∠5
∠4
∠8
∠4 and ∠5

Correct Answer

(1) ∠1 and ∠5
(2) ∠4
(3) ∠4 and ∠5

Explanation

When two lines are cut by a transversal, eight angles are formed. We will consider the relative position of the angles with respect to the two lines and the transversal. There are four pairs of corresponding angles, four interior angles, and two pairs of alternate interior angles.

  1. To identify corresponding angles, we examine the angles to the right of the transversal and the angles to the left of the transversal. The pairs of corresponding angles in the figure are
    • ∠1 and ∠5
    • ∠2 and ∠6
    • ∠4 and ∠8
    • ∠3 and ∠7
  2. To identify the interior angles, we determine the angles inside the two lines cut
    by the transversal. The interior angles in the figure are
    • ∠3, ∠4, ∠5 and ∠6
  3. Alternate interior angles are nonadjacent angles on opposite sides of the transversal inside the two lines. Thus, the pairs of alternate interior angles in the figure are
    • ∠3 and ∠6
    • ∠4 and ∠5

Reference

Mathematics for college students