4) One angle of a right triangle measures \( 60^{\circ} \). What is the measure of the other acute angle?

In a right triangle, the sum of the measures of the three angles is always \(180^{\circ}\). Since one angle is a right angle measuring \(90^{\circ}\) and the other angle is \(60^{\circ}\), we can find the measure of the other acute angle by subtracting both angles from \(180^{\circ}\). That leaves us with \(180^{\circ} - 90^{\circ} - 60^{\circ} = 30^{\circ}\). So, the measure of the other acute angle is \(30^{\circ}\)! Let's not forget the fun part: if you were to draw this triangle, it would embody the classic \(30-60-90\) triangle properties where the side opposite the \(30^{\circ}\) angle is half the length of the hypotenuse, making it a neat little triangle both in math and in aesthetics!