To solve the question regarding two adjacent arcs created by two intersecting diameters in a circle, let's analyze the situation step by step.
1. Equal Measures:
- When two diameters intersect at the center of a circle, they divide the circle into 4 equal parts.
- Each part (arc) is one-quarter of the full circle.
- Since a circle is 360 degrees, each arc measures [tex]\( \frac{360^{\circ}}{4} = 90^{\circ} \)[/tex].
- Therefore, they always have equal measures is true.
2. Difference of Their Measures:
- Since we've established that each arc is 90 degrees and all arcs are equal, the difference between the measures of any two arcs is [tex]\( 90^{\circ} - 90^{\circ} = 0^{\circ} \)[/tex].
- Therefore, the difference of their measures is 90 degrees is false.
3. Sum of Their Measures:
- Adding the measures of any two adjacent arcs: [tex]\( 90^{\circ} + 90^{\circ} = 180^{\circ} \)[/tex].
- Therefore, the sum of their measures is 180 degrees is true.
4. Measures Cannot Be Equal:
- As we've identified, the measures of the arcs are all equal at 90 degrees.
- Therefore, their measures cannot be equal is false.
Summarizing all findings:
- They always have equal measures: True
- The difference of their measures is 90 degrees: False
- The sum of their measures is 180 degrees: True
- Their measures cannot be equal: False
Final numerical result:
(1, 0, 1, 0)
