The measures of the arc are given by the angle subtended in the center of
the circle.
The correct responses are;
- [tex]m\widehat {QT}[/tex] = 120°
- [tex]m\widehat {RT}[/tex] = 60°
- [tex]m\widehat {QRT}[/tex] = 180°
Reasons:
The given parameters are;
The center of circle P = Point P
∠QPS = 15°
The diameter of the circle = RQ
The radii = PS and PT
∠TPS = 105°
Required:
[tex]m\widehat {QT}[/tex]
Solution:
[tex]m\widehat {QT}[/tex] = ∠QPS + ∠TPS by angle addition property
[tex]m\widehat {QT}[/tex] = 15° + 105° = 120°
[tex]m\widehat {QT}[/tex] = 120°
Required:
[tex]m\widehat {RT}[/tex]
Solution:
[tex]m\widehat {RT}[/tex] + ∠QPS + ∠TPS = 180° (The sum of angles on a straight line)
[tex]m\widehat {RT}[/tex] = 180° - (∠QPS + ∠TPS)
[tex]m\widehat {RT}[/tex] = 180° - (15° + 105°) = 60°
[tex]m\widehat {RT}[/tex] = 60°
Required:
[tex]m\widehat {QRT}[/tex]
[tex]m\widehat {QRT}[/tex] = Angle on a straight line (RQ = The diameter) = 180°
[tex]m\widehat {QRT}[/tex] = 180°
Learn more about angle addition postulate here:
https://brainly.com/question/13441938
