Let θ = angle

*APB*

- If
*P* is within the white region, the angle is acute. See *P*_{1}.
- If
*P* is on the red semi-circular curve, the angle is right. See *P*_{2}.
- If
*P* is inside the semi-circular area, the angle is obtuse. See *P*_{3}.

$P = \dfrac{A_\text{semi-circle}}{A_\text{square}}$

$P = \dfrac{\frac{1}{2}\pi (0.5^2)}{1^2}$

$P = \pi / 8$ ← *answer*