When two diameters intersect each other in a circle, they divide the circle into four equal parts. Each of these parts represents an arc of the circle.
Let's analyze the steps:
1. A full circle has an angle measure of [tex]\(360^{\circ}\)[/tex].
2. When one diameter is drawn, it divides the circle into two semicircles, each with an angle measure of [tex]\(180^{\circ}\)[/tex].
3. When a second diameter intersects the first diameter at right angles (perpendicularly), it further divides each of those semicircles into two equal quarters.
4. Therefore, each quarter-circle or arc created by the intersection of two diameters has an angle measure of [tex]\(90^{\circ}\)[/tex].
5. If we consider two adjacent arcs (which are next to each other), each of these arcs will measure [tex]\(90^{\circ}\)[/tex].
6. Adding the measures of these two adjacent arcs together:
[tex]\[90^{\circ} + 90^{\circ} = 180^{\circ}\][/tex]
Therefore, the correct statement about the two adjacent arcs created by two intersecting diameters is:
c) The sum of their measures is [tex]\(180^{\circ}\)[/tex].
