If two straight lines intersect each other, prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Explanation

To prove that the ray opposite to the bisector of one of the angles formed by two intersecting lines bisects the vertically opposite angle, we can follow these steps:

### Step 1: Understand the Configuration
Let two straight lines intersect at point O, forming angles ∠AOB, ∠BOC, ∠COD, and ∠DOA. Assume that ray OP is the bisector of angle ∠AOB. We need to prove that ray OQ, which is opposite to OP, bisects the angle ∠COD.

### Step 2: Define the Angles
Let:
- ∠AOB = angle 1
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