1. **Problem Statement:** Find the azimuths of lines AB, BC, CD, and DA given angles between these lines and cardinal directions at points A, B, C, and D. 2. **Understanding Azimuths:** Azimuth is the angle measured clockwise from the North direction to the line. 3. **Given Data:** - At B: angle between AB and North is 25° - At B: angle between BC and West is 68° - At C: angle between CD and South is 17° - At D: angle between DA and East is 62° - At A: angle between DA and North is 25° - At A: angle between AB and West is 62° 4. **Calculate Azimuth of AB:** - At B, AB is 25° from North, so azimuth of AB at B is $25^\circ$. - At A, AB is 62° from West. Since West is 270° from North, azimuth at A is $270^\circ + 62^\circ = 332^\circ$. - Since azimuth is consistent along the line, average or verify direction. Here, AB azimuth is $332^\circ$ (from A) or $25^\circ$ (from B). Because 332° is equivalent to -28° (clockwise from North), the correct azimuth is $25^\circ$ (from B) or $332^\circ$ (from A), which are opposite directions. We take azimuth of AB as $25^\circ$. 5. **Calculate Azimuth of BC:** - At B, BC is 68° from West. - West is 270°, so azimuth of BC at B is $270^\circ - 68^\circ = 202^\circ$ (since angle is clockwise from West to BC). 6. **Calculate Azimuth of CD:** - At C, CD is 17° from South. - South is 180°, so azimuth of CD at C is $180^\circ + 17^\circ = 197^\circ$. 7. **Calculate Azimuth of DA:** - At D, DA is 62° from East. - East is 90°, so azimuth of DA at D is $90^\circ - 62^\circ = 28^\circ$. - At A, DA is 25° from North, so azimuth of DA at A is $25^\circ$. - Both values are close, so azimuth of DA is approximately $25^\circ$ to $28^\circ$. **Final Azimuths:** - AB: $25^\circ$ - BC: $202^\circ$ - CD: $197^\circ$ - DA: $25^\circ$ to $28^\circ$ (approximate) These azimuths represent the clockwise angle from North to each line.