Question

estimate the measure of this angle within 15°. angle image

Explanation:

Step1: Recall angle types

A straight angle is \(180^\circ\), a right angle is \(90^\circ\). The given angle is obtuse (greater than \(90^\circ\), less than \(180^\circ\)).

Step2: Estimate the angle

Compare with known angles. A \(135^\circ\) angle is halfway between \(90^\circ\) and \(180^\circ\) in a sense, but this angle looks like \(135^\circ\) or closer to \(120^\circ - 150^\circ\). The angle here, visually, is about \(135^\circ\) (within \(15^\circ\) of \(135^\circ\), so \(120^\circ - 150^\circ\) range, but a good estimate is \(135^\circ\) or \(120^\circ\), \(150^\circ\). But more accurately, the angle between the two rays: one going right, one going up - left. The angle is obtuse, and by visual estimation, it's approximately \(135^\circ\) (or \(120^\circ\), \(150^\circ\) within \(15^\circ\) error). A common estimate for this type of angle (a reflex - no, obtuse) angle is \(135^\circ\), or \(120^\circ\), \(150^\circ\). But the most probable estimate within \(15^\circ\) is \(135^\circ\) (or \(120^\circ\) to \(150^\circ\), but a typical answer is \(135^\circ\) or \(120^\circ\), \(150^\circ\)). Wait, actually, the angle is like a \(135^\circ\) angle (since it's 3/4 of a straight angle? No, a straight angle is \(180^\circ\), a right angle \(90^\circ\). The angle here is between a horizontal ray (right) and a ray going up - left, making an angle that's \(135^\circ\) (because from horizontal, going up - left at \(135^\circ\) from the positive x - axis). So estimating, it's about \(135^\circ\) (within \(15^\circ\), so \(120^\circ\) to \(150^\circ\) is acceptable, but a precise estimate is \(135^\circ\)).

Answer:

\(135^\circ\) (or \(120^\circ\), \(150^\circ\) within \(15^\circ\) error, but a common answer is \(135^\circ\))