Question

estimate the measure of this angle within 15°.

Explanation:

Step1: Recall angle types

An acute angle is less than \(90^{\circ}\), a right angle is \(90^{\circ}\), and an obtuse angle is greater than \(90^{\circ}\) but less than \(180^{\circ}\). This angle is acute.

Step2: Estimate within \(15^{\circ}\)

Common reference angles: \(30^{\circ}\) (narrower, like a sharp corner), \(45^{\circ}\) (half - way between \(0^{\circ}\) and \(90^{\circ}\) in a sense of slope), \(60^{\circ}\) (steeper than \(45^{\circ}\)). This angle looks steeper than \(45^{\circ}\) but less than \(75^{\circ}\). A reasonable estimate is \(60^{\circ}\) (since \(60^{\circ}\pm15^{\circ}\) gives a range \(45^{\circ}-75^{\circ}\) and the angle fits in this range).

Answer:

\(60^{\circ}\)