Answer :
Answer:
The correct answer is:
d. the arc measurement of the given angle
Explanation:
When a central angle of a circle measures 42 degrees, it signifies both the angle's magnitude and the arc's measurement it spans. The arc measurement mirrors the angle's value, in this case, 42 degrees. This correspondence is a fundamental property of central angles within circles, where the angle's measure directly relates to the length of the arc it subtends. Therefore, in this scenario, the arc measurement of the given angle also equals 42 degrees, illustrating the intrinsic relationship between angles and arcs in circular geometry.
The arc measurement of the given angle (42 degrees) and the arc measurement of the vertical angle are both 42 degrees, corresponding to the central angle of a circle. Hence, options d and f are the correct answers.
According to Theorem, angles at the center of a circle are proportional to the intercepted arcs and can be measured by them. Since a central angle of a circle measures 42 degrees, its corresponding arc also measures 42 degrees because one degree corresponds to an arc of one degree in a circle.
In response to the student's question, d. the arc measurement of the given angle is correct as it is directly proportional to the central angle, and both measure 42 degrees. Vertical angles are also the same as the angle they are vertical to, so f. the arc measurement of the vertical angle is also 42 degrees. Options a, b, c, e, and g do not correctly relate to the degree measure of the arc created by a 42-degree central angle in a circle.
