Question

what compass heading represents 20° north of west?
?°
hint: compass headings are measured from north, going clockwise.

Explanation:

Step1: Understand Compass Heading

Compass headings start at north (0°) and rotate clockwise. West is 270° from north, but we need 20° north of west.

Step2: Calculate the Heading

North is 0°, west is 270° clockwise from north. But "north of west" means we start from west and move 20° towards north. So from north, moving clockwise, west is 270°, but north of west is 180° - 20°? Wait, no. Wait, clockwise from north: north is 0°, east is 90°, south is 180°, west is 270°. But "north of west" means the angle between west and the direction is 20° towards north. So from north, clockwise, the angle would be 180° + (90° - 20°)? Wait, no. Let's think again. West is 270° clockwise from north. North of west: so we are 20° towards north from west. So the angle from north clockwise would be 270° - 20°? Wait, no. Wait, if you are north of west, the direction is between north and west. So from north, turning towards west, 20° towards west? No, "north of west" means closer to north than to west. Wait, the hint says compass headings are measured from north, going clockwise. So north is 0°, east is 90°, south is 180°, west is 270°. Now, "20° north of west" means that the angle between the direction and west is 20°, towards north. So from west (270°), moving 20° towards north (which is counter-clockwise), but we need clockwise from north. So the angle from north clockwise would be 270° - 20° = 250°? Wait, no. Wait, if you are north of west, the direction is 20° towards north from west. So west is 270° clockwise from north. Moving towards north (counter-clockwise) 20° from west would be 270° - 20° = 250° clockwise from north. Let's verify: north is 0°, east 90°, south 180°, west 270°. North of west: so between north (0°) and west (270°)? No, wait, directions: north, northeast, east, southeast, south, southwest, west, northwest. Wait, northwest is 45° north of west? No, northwest is 45° between north and west. Wait, maybe I messed up. Let's use the standard: compass heading is measured clockwise from north. So north is 0°, east is 90°, south is 180°, west is 270°. Now, "20° north of west" means that the angle between the direction and west is 20°, with the direction being closer to north. So from west (270°), moving 20° towards north (which is a counter-clockwise direction), but since we measure clockwise from north, we need to find the clockwise angle. So the angle from north clockwise to the direction: west is 270°, so moving 20° towards north (counter-clockwise) from west is 270° - 20° = 250°? Wait, no. Wait, if you are north of west, the direction is in the northwest quadrant, 20° towards north from west. So the angle from north clockwise would be 180° + (90° - 20°) = 180° + 70° = 250°? Wait, 180° is south, 90° from south to west is 90°, so 180° + 90° is 270° (west). So 20° north of west is 270° - 20° = 250°? Wait, let's take an example: 45° north of west (northwest) would be 270° - 45° = 225°? No, that can't be. Wait, no, 45° north of west: from north, clockwise, 180° - 45° = 135°? No, that's southeast. Wait, I'm confused. Wait, let's use the formula: for a direction that is θ° north of west, the compass heading (clockwise from north) is 180° + (90° - θ°) = 270° - θ°. Wait, θ is 20°, so 270° - 20° = 250°. Yes, that makes sense. Because west is 270°, north of west is towards north, so subtract the angle from west towards north. So 270° - 20° = 250°.

Answer:

250