Question

question 32 (1 point)
an angle drawn in standard position
a) must be less than 90°.
b) must be less than 180°.
c) must be less than 360°.
d) can be any number of degrees

Explanation:

Step1: Recall the definition of an angle in standard position

An angle in standard position is formed by rotating a ray about its endpoint. The measure of an angle in standard position can range from \(0^{\circ}\) to \(360^{\circ}\). But when we draw an angle (in the context of basic geometric angles we usually consider for non - full - rotation angles), the angle we are referring to (the non - reflex part when considering a rotation) must be less than \(180^{\circ}\). Angles greater than or equal to \(180^{\circ}\) are reflex angles. When we talk about "an angle drawn in standard position" in a general geometric sense (not considering full rotations and reflex angles for the basic drawing and measurement concept), we consider angles in the range \(0^{\circ}<\theta < 180^{\circ}\).

• Option a: Angles less than \(90^{\circ}\) are acute angles. But there are also right (\(90^{\circ}\)) and obtuse (\(90^{\circ}<\theta<180^{\circ}\)) angles that are valid when drawn in standard position. So this option is too restrictive.
• Option b: Angles must be less than \(180^{\circ}\). This is correct because if \(\theta = 180^{\circ}\) it is a straight angle (a special case, but when we "draw" an angle in the non - straight - line - representing - a - full - half - rotation sense for basic angle drawing in standard position, we consider non - straight angles as well, and in general, the measure of the non - reflex angle (the one we focus on for basic geometric drawing) is less than \(180^{\circ}\)).
• Option c: Angles can be \(180^{\circ}\) (straight angle) or less. But when we draw an angle (in the non - straight - line - as - a - special - case - for - basic - angle - drawing - emphasis), we usually consider angles less than \(180^{\circ}\) (excluding the straight angle in the basic "drawing an angle" concept where we focus on non - straight, non - full - rotation - related angles). Also, angles greater than \(180^{\circ}\) are reflex angles which are not the primary focus for a general "drawn angle" in standard position (in basic geometry).
• Option d: Angles have a range. But in the context of a general "drawn angle" (not considering full rotations and reflex angles for basic geometric drawing), it is not "any number".

Answer:

b) must be less than \(180^{\circ}\)