Question

which of the following statements best describes an angle that is in standard position?
select the correct choice below.
a. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive y - axis.
b. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the negative x - axis.
c. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the negative y - axis.
d. an angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x - axis.

Explanation:

To determine the correct description of an angle in standard position, we recall the definition: an angle is in standard position when its vertex is at the origin of a rectangular coordinate system, and its initial side lies along the positive x - axis.

• Option A: The initial side is said to lie along the positive y - axis, which is incorrect.
• Option B: The initial side is said to lie along the negative x - axis, which is incorrect.
• Option C: The initial side is said to lie along the negative y - axis, which is incorrect.
• Option D: Matches the definition of an angle in standard position (vertex at origin, initial side along positive x - axis).

Answer:

D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x - axis.