24 Degree Angle

A 24° angle is an acute angle: it is smaller than a right angle (90°). It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 66°.

24° is one fifteenth (1/15) of a full circle, or 2π/15 radians. The minute hand of a clock sweeps 24° in 4 minutes. If you face north and turn 24° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).

24° angle facts

Trigonometric values of 24°

24° on a protractor

How to draw a 24° angle with a protractor

1. Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
2. Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
3. Find 24° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
4. Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 24°.

Drawing it a 24° angle without a protractor (rise and run method)

1. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
2. At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
3. Measure 4.45 inches (about 4 7/16″) up that line and make a mark.
4. Join the mark to the vertex. The angle at the vertex is 24°, because tan 24° ≈ 0.4452.

Where you see 24° angles

• Divide a circle into 15 equal slices and each slice is 24°, e.g. 15 spokes on a wheel or 15 equal pie-chart wedges.
• A board sloped at 24° rises about 53.4 inches over a 10-foot (120-inch) run.
• 24° of latitude on Earth spans roughly 1,657 miles north to south.
• The Earth turns 24° on its axis in about 1 h 36 min.

Related angles

• Complement: 66°
• Supplement: 156°
• Explement: 336°
• Half: 12°
• Double: 48°
• 30°
• 45°
• 60°
• 90°