A 174° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 6°, so a 174° angle and a 6° angle side by side make a straight line.
174° is 29/60 of a full circle, or 29π/30 radians. The minute hand of a clock sweeps 174° in 29 minutes. If you face north and turn 174° clockwise, you end up facing between SSE and S (closest to south (S)).
174° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 6° |
| Explement (adds to 360°) | 186° |
| Radians | 29π/30 ≈ 3.036873 |
| Gradians | 193.3333 grad |
| Fraction of a turn | 29/60 (48.33%) |
| Degrees, minutes, seconds | 174° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south (S)) |
Trigonometric values of 174°
| Function | Value |
|---|---|
| sin 174° | 0.104528 |
| cos 174° | −0.994522 |
| tan 174° | −0.105104 |
174° on a protractor
How to draw a 174° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 174° 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.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 174°.
Drawing it a 174° angle without a protractor (rise and run method)
- 174° = 180° − 6°. Draw a straight line, pick a vertex on it, and build a 6° angle on one side as follows; the angle on the other side of the new line is 174°.
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- 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).
- Measure 1.05 inches (about 1 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 6°, because tan 6° ≈ 0.1051.
Where you see 174° angles
- Each interior corner of a regular 60-sided polygon measures 174°.
- The Earth turns 174° on its axis in about 11 h 36 min.
- Obtuse angles like 174° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
174° angle FAQ
What type of angle is 174°?
A 174° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 174°?
The supplement of 174° is 6°, because 174° + 6° = 180°. A 174° angle has no complement, because it is already larger than 90°.
How many radians is 174 degrees?
174° = 29π/30 radians ≈ 3.0369 rad. To convert degrees to radians, multiply by π/180: 174 × π/180 = 29π/30.
How do I measure a 174° angle on my screen?
Open the online protractor with 174° preset, or type 174 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
