Two chords that intersect within a circle form an angle whose measure is 55°. If this angle’s arc is 100°, what is the measure of the arc of its vertical angle?

To find the measure of the arc of the vertical angle, we can use the properties of angles formed by intersecting chords within a circle.

The angle formed by the two chords is 55°, and we know that this angle's arc is 100°. Let's call the arc of the vertical angle x°.

According to the properties of angles formed by intersecting chords, the measure of an angle is equal to half the measure of its intercepted arc.

Since the angle formed by the two chords is 55°, the intercepted arc is twice as large, which is 2 * 55° = 110°.

Now, we can set up an equation:

x° = 110° - 100°
x° = 10°

Therefore, the measure of the arc of the vertical angle is 10°.

To find the measure of the arc of the vertical angle, we need to first understand the relationship between the angle formed by the two intersecting chords and the arcs of the circle.

When two chords intersect within a circle, the angles formed are called vertical angles. These angles are always equal in measure. Therefore, the angle opposite the given 55° angle will also measure 55°.

Now, since the angle’s arc measures 100°, we know that the arc opposite this angle will also measure 100°. This is because an inscribed angle (formed by two intersecting chords) will always measure half the measure of its intercepted arc.

Since we are looking for the arc of the vertical angle, which is the same as the arc opposite the 55° angle, we can conclude that its measure is also 100°.