1. **Problem statement:** Calculate the bearing of point Y from point Z given the angles at points X and Y relative to north. 2. **Understanding bearings:** A bearing is measured clockwise from north. The angle at X is 125°, meaning the line ZX is 125° clockwise from north at X. The angle at Y is 105°, meaning the line YZ is 105° clockwise from north at Y. 3. **Goal:** Find the bearing of Y from Z, i.e., the angle clockwise from north at Z to the line ZY. 4. **Step 1: Analyze the triangle XYZ.** The points form a triangle with known angles relative to north at X and Y. 5. **Step 2: Calculate the interior angle at Z.** The interior angles of triangle XYZ sum to 180°. 6. **Step 3: Use the given angles to find the interior angles of the triangle.** - The angle at X between north and ZX is 125°, so the interior angle at X is $180^\circ - 125^\circ = 55^\circ$. - The angle at Y between north and YZ is 105°, so the interior angle at Y is $180^\circ - 105^\circ = 75^\circ$. 7. **Step 4: Calculate the interior angle at Z:** $$ \text{Angle at Z} = 180^\circ - 55^\circ - 75^\circ = 50^\circ $$ 8. **Step 5: Calculate the bearing of Y from Z.** - The bearing at Z is the angle clockwise from north to line ZY. - Since the interior angle at Z is 50°, and the north direction is vertical, the bearing of Y from Z is: $$ \text{Bearing} = 360^\circ - 50^\circ = 310^\circ $$ 9. **Final answer:** The bearing of Y from Z is **310°**.