Answer:
The required angles are;
Central angle measure is 176°
Inscribed angle measure is 88°
Circumscribed angle measure is 4°
Step-by-step explanation:
Here we have;
Sum of angle at center + opposite circumscribed angle = 180
From circle theorem, angle at the center = 2 × Angle at circumference
Therefore, for maximum angle at the center, we have;
Angle at the center → 180°
Where angle at the center = 180°
Therefore, circumscribed angle = 180° - 180° = 0°
Again
2 × Angle at the circumference = angle at the center
∴ 2 × Angle at the circumference = 180°
∴ Angle at the circumference = 90°
Hence,
Central angle measure = 180°
Inscribed angle measure = 90°
Circumscribed angle measure = 0°
However, using the digit from 0 to 9 at most 1 time each, we have, counting down from 180° and comparing
Central angle measure = 176°
Inscribed angle measure = 88°
Circumscribed angle measure = 4°.
