Answer :
To determine the properties of two adjacent arcs created by two intersecting diameters within a circle, let's analyze the situation step-by-step.
1. Understanding the Setup:
- A circle is a shape with 360 degrees.
- A diameter is a straight line passing through the center of the circle, thus dividing the circle into two equal parts, each of 180 degrees.
2. Intersecting Diameters:
- When two diameters intersect at the center of the circle, they divide the circle into four equal parts.
- Each part thus represents 360 degrees divided by 4, which is 90 degrees.
3. Adjacent Arcs:
- Since the circle is divided into four equal arcs (each 90 degrees), two adjacent arcs each measure 90 degrees.
- Adjacent arcs mean the arcs that are next to each other and share a common endpoint.
4. Sum of Their Measures:
- For two adjacent arcs, their measures ad up to \(90^{\circ} + 90^{\circ} = 180^{\circ}\).
Based on this detailed analysis, the correct statement is:
- The sum of their measures is \(180^{\circ}\).
So the true statement regarding two adjacent arcs created by two intersecting diameters is:
The sum of their measures is [tex]\(180^{\circ}\)[/tex].
1. Understanding the Setup:
- A circle is a shape with 360 degrees.
- A diameter is a straight line passing through the center of the circle, thus dividing the circle into two equal parts, each of 180 degrees.
2. Intersecting Diameters:
- When two diameters intersect at the center of the circle, they divide the circle into four equal parts.
- Each part thus represents 360 degrees divided by 4, which is 90 degrees.
3. Adjacent Arcs:
- Since the circle is divided into four equal arcs (each 90 degrees), two adjacent arcs each measure 90 degrees.
- Adjacent arcs mean the arcs that are next to each other and share a common endpoint.
4. Sum of Their Measures:
- For two adjacent arcs, their measures ad up to \(90^{\circ} + 90^{\circ} = 180^{\circ}\).
Based on this detailed analysis, the correct statement is:
- The sum of their measures is \(180^{\circ}\).
So the true statement regarding two adjacent arcs created by two intersecting diameters is:
The sum of their measures is [tex]\(180^{\circ}\)[/tex].
