What is the measure of arc QSR?
S
70°
The Correct Answer and Explanation is :
The correct answer is: {Measure of arc } QSR = 70°
To determine the measure of arc ( QSR ), we need to consider the context in which this arc is defined, typically within a circle. The measure of an arc is usually related to the angle subtended at the center of the circle by the endpoints of the arc.
In this case, we have a central angle ( S ) measuring ( 70° ).
Explanation
- Understanding Arcs and Angles:
- An arc is a portion of the circumference of a circle, defined by two endpoints (in this case, points ( Q ) and ( R )) and includes the center of the circle ( S ).
- The measure of an arc is usually equal to the measure of the central angle that subtends that arc. Therefore, if ( S ) is the vertex of the angle and it subtends arc ( QSR ), then the measure of arc ( QSR ) will be equal to the measure of the angle ( S ).
- Calculation:
- Given that the angle ( S ) is ( 70° ), the measure of the arc ( QSR ) will also be ( 70° ). This is because the arc length is directly related to the angle at the center of the circle that spans that arc.
- Real-Life Application:
- This concept is essential in various applications, including engineering, architecture, and navigation, where understanding the properties of circles and angles is crucial for design and analysis. For instance, if one were designing a circular path, knowing the arc measure can help determine how much space the path will occupy.
- Conclusion:
- In summary, the measure of arc ( QSR ) is equal to the measure of angle ( S ), which is ( 70° ). This fundamental relationship between central angles and their corresponding arcs is a cornerstone of circle geometry. Thus, the final answer is:
[
\text{Measure of arc } QSR = 70°.
]