73.

In the figure, D is the centre of a circle. Prove that
2(∠XZY + ∠YXZ) = ∠XPZ]

Given: P is the centre of a circle.
To prove: 2(∠XZY + ∠YXZ) = ∠XPZ
Proof: ∠XPY = 2∠XZY    ...(1)
| The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any point on the remaining part of the circle
∠YPZ = 2 ∠YXZ    ...(2)
| The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any point on the remaining part of the circle
Adding (1) and (2), we get,
∠XPY + ∠YPZ = 2 ∠XZY + 2 ∠YXZ
⇒    ∠XPZ = 2 (∠XZY + ∠YXZ)
⇒ 2 (∠XZY + ∠YXZ) = ∠XPZ.