Question

In the diagram, how many angles must be supplementary with angle 14?

4 lines intersect to form 16 angles. The angles created, clockwise from top left are 1, 2, 3, 4; 5, 6, 7, 8; 13, 14, 15, 16; 9, 10, 11, 12.
one
two
four
eight

Answer 1

To determine how many angles must be supplementary with angle 14, we first need to identify the angles that are formed around angle 14 in the context of the intersecting lines.

Supplementary angles are defined as angles that sum up to 180 degrees. In the case of four lines intersecting to form 16 angles, angle 14 is part of a set of interior angles adjacent to it.

Looking clockwise from angle 14, the angles that are adjacent (and thus supplementary) to angle 14 are:

- Angle 15 (to the right of angle 14)
- Angle 13 (to the left of angle 14)
- Angle 8 (below angle 14)
- Angle 6 (above angle 14)

These neighboring angles can pair with angle 14 to form supplementary angle relationships. Specifically:

1. Angle 14 and angle 15
2. Angle 14 and angle 13
3. Angle 14 and angle 8
4. Angle 14 and angle 6

Thus, there are **four angles** that must be supplementary with angle 14.

The correct answer is **four**.