Question

Identifying Supplementary Angles
Examine the intersection of these two lines:

2 lines intersect to form 4 angles. From the top, clockwise, the angles are 1, 4, 2, 3.

Which of the following pairs of angles are supplementary? Select all that apply.
∠1 and ∠2
∠1 and ∠3
∠1 and ∠4
∠2 and ∠3
∠2 and ∠4
∠3 and ∠4

Answer 1

Adjacent angles formed by intersecting lines are supplementary (sum to 180°); vertical (opposite) angles are equal, not supplementary. With the labels given (top = 1, right = 4, bottom = 2, left = 3), the supplementary pairs are:

- ∠1 and ∠3 — yes
- ∠1 and ∠4 — yes
- ∠2 and ∠3 — yes
- ∠2 and ∠4 — yes

The pairs that are not supplementary are ∠1 and ∠2 (vertical) and ∠3 and ∠4 (vertical).