In the following figure, O is the center of the circle. Find the value of d.

We know that,

Angle in semi-circle is a right angle.

∴ ∠APB = 90°

In △APB,

⇒ ∠APB + ∠PBA + ∠PAB = 180°

⇒ 90° + 45° + ∠PAB = 180°

⇒ ∠PAB = 180° - 135° = 45°.

We know that,

Angles subtended by the same chord on the circle are equal.

∴ d = ∠PAB = 45°.

Hence, d = 45°.