Question

what are two possible measures of the angle below?
-120° and 90°
-120° and 75°
-270° and 90°
-270° and 45°

Explanation:

To solve this, we analyze the angle measures. A vertical line (along the y - axis) and a horizontal line (along the x - axis) form a right angle of \(90^{\circ}\). The other angle, when considering the full - circle or supplementary/related angle concepts, if we have a line that makes a \(270^{\circ}\) angle (a reflex angle) and a \(90^{\circ}\) angle (the right angle between the axes), this makes sense. Let's check the options:

• Option 1: \(- 270^{\circ}\) and \(45^{\circ}\) do not relate to the axes' angle relationship.
• Option 2: \(-270^{\circ}\) (which is equivalent to \(90^{\circ}\) in terms of the angle between the axes when considering direction and standard position, since \(-270^{\circ}+360^{\circ}=90^{\circ}\)) and \(90^{\circ}\) fit the angle relationship between the vertical and horizontal lines (the axes) in the diagram.
• Option 3: \(-120^{\circ}\) and \(75^{\circ}\) do not match the right - angle relationship of the axes.
• Option 4: \(-120^{\circ}\) and \(90^{\circ}\) also do not match the angle relationship we observe from the axes.

Answer:

\(-270^{\circ}\) and \(90^{\circ}\) (the second option in the given choices, i.e., the option with \(-270^{\circ}\) and \(90^{\circ}\))