1. **Problem Statement:** We have two roads: the first road (I. road) is horizontal, and the second road (II. road) is diagonal. Point A lies on the first road, and point B lies on the second road. The path from A to B involves turning angles of 40°, 80°, and 50°, with a right angle at the junction near B. We want to analyze the geometry and find relevant distances or angles. 2. **Understanding the Angles and Roads:** - The first road is horizontal, so it lies along the East-West direction. - The second road is diagonal, forming an angle with the horizontal. - The turning angles 40°, 80°, and 50° sum to 170°, which suggests the path changes direction at these angles. - The right angle at the junction near B indicates a 90° angle between the second road and the path segment near B. 3. **Using Triangle Angle Sum Rule:** In the triangle formed by points A, B, and the junction, the sum of interior angles is 180°. Given angles 40°, 80°, and 50°, and a right angle (90°) at the junction, we can analyze the triangle formed. 4. **Applying Trigonometry:** If we denote the length from A to the junction as $x$ and from the junction to B as $y$, and the angle between roads as $\theta$, we can use the Law of Sines or Cosines to find unknown lengths or angles. 5. **Summary:** - The problem involves understanding the geometry of two roads intersecting with given angles. - The right angle at the junction helps establish perpendicularity. - Using angle sum and trigonometric laws, distances or directions can be calculated. Since no specific question or values to find were given, this is the geometric interpretation and approach to solve such a problem.