Thank you for visiting Complete the statements about circle z A central angle such as angle angle UZV of circle z is an angle whose vertex is the center. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer:
A central angle, such as angle
UZV
of circle
Z
, is an angle whose vertex is
the center of the circle
and whose sides are radii of the circle.
Angle
WSX
is not a central angle of circle
Z
.
The degree measure of an arc is
equal to
the degree measure of the central angle that intercepts it.
The measure of
\overarc
TU
is
79
degrees.
Step-by-step explanation:
Definition of Central Angle:
A central angle, such as angle UZV of circle Z, is an angle whose vertex is the center of the circle, and whose sides are radii of the circle.
Angle WSX is Not a Central Angle:
Angle WSX is not a central angle of circle Z.
Degree Measure of an Arc:
The degree measure of an arc is equal to the degree measure of the central angle that intercepts it.
Measure of
\overarc
�
�
\overarcTU:
The measure of
\overarc
�
�
\overarcTU is 79 degrees.
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Rewritten by : Jeany
Final answer:
The question addresses central angles and arc lengths in circles, focusing on how the degree measure of an arc relates to its central angle and how angles are measured in radians in terms of rotations and arc lengths.
Explanation:
The student's question revolves around the concept of central angles and arc lengths in a circle. To clarify, a central angle is an angle whose vertex is the center of the circle, and its sides are made up of two radii. Considering a central angle angle UZV as described in the question, this angle determines the arc it intercepts. If the measure of angle UZV is 79 degrees, it means that the arc length corresponding to this angle would be a portion of the circumference of the circle proportional to the angle's size relative to 360 degrees, the full angle measure of a circle.
Additionally, the degree measure of an arc is directly related to the degree measure of its central angle. If angle WSX is not a central angle, its relationship to the arc it subtends would differ from that of a central angle. When we consider rotations and their corresponding arc lengths, we often describe the angle of rotation in radians, where 2π radians is equal to one full revolution (360 degrees) around the circle.
In terms of arc length, when a radius r is rotated through an angle, the resulting arc length (Δs) can be calculated using the formula Δθ = Δs / r, where Δθ represents the angle of rotation in radians and Δs the arc length.
