Angle APB and angle AOB are subtended by the same arc [tex]\mathbf{\widehat{AB}}[/tex] on the
circumference.
Correct response:
- The measure of angle APS is 52°
Use of circle theorems to find the measure of angles
The given parameters are;
Points A, B, and P are on the circumference of the circle
∠OBA = 38°
Required:
The measure of ∠APB
Solution:
Segments OB and OA are radii of the circle
Therefore;
OB = OA
ΔAOB = An isosceles triangle
Which gives;
∠ABO = ∠BAO = 38°
∠AOB = 180° - (∠ABO + ∠BAO)
Therefore;
∠AOB = 180° - (38° + 38°) = 104°
∠AOB = 104°
According to circle theorem, we have;
Angle subtended at center = 2 × Angle subtended at the circumference
Therefore;
∠AOB = 2 × ∠APB
Therefore;
104° = 2 × ∠APB
Which gives;
[tex]\angle APB = \dfrac{104^{\circ}}{2} = \mathbf{ 52^{\circ}}[/tex]
Learn more about circle theorem here:
https://brainly.com/question/16879446
