The angle subtended by an arc [tex]\widehat{AU}[/tex] is given by the angle ∠UOA.
Response:
- [tex]\widehat{AU}[/tex] is 50°
Which methods can be used to find [tex]\widehat{AU}[/tex] ?
According to circle theorem, we have;
- Angle at the center = 2 × Angle at the circumference
∠QUA = 111°
Therefore;
[tex]m\widehat{QDA}[/tex] = 2 × ∠QUA
[tex]m\widehat{QDA}[/tex] = 2 × 111° = 222°
Which gives;
Angle ∠QOA = [tex]m\widehat{QUA}[/tex] = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA by angle addition property
Which gives;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
- [tex]\widehat{AU}[/tex] = ∠UOA = 50°
Learn more about more circle theorems here:
https://brainly.com/question/23665463
