To determine the truth about two adjacent arcs created by two intersecting diameters, let's break down some key geometrical principles related to the situation.
1. Definition of Diameters and Arcs:
- A circle consists of 360 degrees in total.
- A diameter divides a circle into two equal semicircles of 180 degrees each.
- When two diameters intersect at a right angle, they create four arcs in the circle.
2. Creating Arcs:
- Each of these intersections creates four arcs of 90 degrees each, as each quarter of the circle is 90 degrees.
- Two adjacent arcs are created by two halves of a 180-degree semicircle.
3. Adjacent Arcs' Relationship:
- Two adjacent arcs, in this case, are both created by the intersection of these diameters.
- Because each quarter arc is 90 degrees, when you sum the measures of two adjacent arcs, it always amounts to:
[tex]\[
90^{\circ} + 90^{\circ} = 180^{\circ}
\][/tex]
4. Answer to the Question:
- The sum of the measures of two adjacent arcs created by two intersecting diameters is always [tex]\(180^{\circ}\)[/tex].
Therefore, the correct statement about two adjacent arcs created by two intersecting diameters is:
The sum of their measures is [tex]\(180^{\circ}\)[/tex].
