Question

estimate the measure of this angle within 15°.

Explanation:

Step1: Recall angle - type characteristics

An acute angle is between \(0^{\circ}\) and \(90^{\circ}\), a right - angle is \(90^{\circ}\), and an obtuse angle is between \(90^{\circ}\) and \(180^{\circ}\). The given angle is acute.

Step2: Make an estimate

We know that \(45^{\circ}\) is a common acute - angle benchmark. The given angle is larger than \(30^{\circ}\) (since \(30^{\circ}\) is a relatively small acute angle) and smaller than \(60^{\circ}\). A reasonable estimate within \(15^{\circ}\) is \(60^{\circ}\) (because \(60 - 15=45\) and \(60 + 15 = 75\), and the angle is in the range where \(45^{\circ}<\text{angle}<75^{\circ}\)).

Answer:

\(60\)