5. In the figure above, the circle has center O. If the measure of arc APB is 56°, what is the value of x?
Answer: C
x = 56°
The value of x is equal to 56°, which corresponds to the measure of arc APB in the circle with center O.
A) 28
Option A is incorrect because 28° does not reflect the measure of arc APB. The relationship between the arc's measure and angles in the circle clearly indicates that x should be directly associated with the arc's measure.
B) 34
Option B is incorrect as well. A measure of 34° does not align with the given arc measurement of 56°. The value of x must represent the full extent of arc APB, which is not satisfied by this option.
C) 56
Option C is correct because it accurately matches the measure of arc APB, which is given as 56°. Since x is defined in relation to this arc, it follows that x equals the arc's measure.
D) 62
Option D is incorrect because 62° exceeds the measure of arc APB. The problem specifies that x must be equal to the arc's measure, making 62° an invalid choice.
Conclusion
The correct answer, 56°, is the only option that correctly corresponds to the measure of arc APB, directly fulfilling the requirements of the question. All other options either underestimate or overestimate the arc's measure, reinforcing that 56° is the definitive value for x.