Question

the piece of art below was created with strings of different lengths strung in straight - line segments across the canvas. angle 1 and angle 2 are formed by the intersection of different strings, but both angles have a measure of 72°. which statement about the geometric relationships formed by the strings in the art must be true? angle 1 and angle 2 are complementary angles. angle 1 and angle 2 are vertical angles. line f and line n are perpendicular. line s and line t are parallel.

Explanation:

Step1: Recall angle - relationship definitions

Complementary angles add up to 90°. Since \(72^{\circ}+72^{\circ}=144^{\circ}
eq90^{\circ}\), angle 1 and angle 2 are not complementary.

Step2: Recall vertical - angle definition

Vertical angles are formed by the intersection of two lines and are opposite each other. Angle 1 and angle 2 are formed by the intersection of different strings and are equal in measure, and they are vertical angles.

Step3: Analyze perpendicular - line condition

There is no indication that the measure of the angle between line \(f\) and line \(n\) is 90°, so we cannot say they are perpendicular.

Step4: Analyze parallel - line condition

There is no information about the relationship between line \(s\) and line \(t\) (such as corresponding angles, alternate - interior angles etc.) to conclude they are parallel.

Answer:

Angle 1 and Angle 2 are vertical angles.