c An angle 2 Two chords intersect inside a circle andform an angle of \( 75^{\circ} \). If one of the intercepted arc is \( 60^{\circ} \), find the measure of the other intercepted arc.

To find the measure of the other intercepted arc, we can use the property of angles formed by intersecting chords in a circle. The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the intercepted arcs. Since the angle is \( 75^{\circ} \) and one of the intercepted arcs is \( 60^{\circ} \), we denote the measure of the other intercepted arc as \( x \). Using the formula: \[ 75^{\circ} = \frac{1}{2} (60^{\circ} + x) \] Multiplying both sides by 2 gives us: \[ 150^{\circ} = 60^{\circ} + x \] Now, subtract \( 60^{\circ} \) from both sides: \[ x = 150^{\circ} - 60^{\circ} = 90^{\circ} \] Thus, the measure of the other intercepted arc is \( 90^{\circ} \).