A 342° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of an 18° angle: together they make a full 360° circle.
342° is 19/20 of a full circle, or 19π/10 radians. The minute hand of a clock sweeps 342° in 57 minutes. If you face north and turn 342° clockwise, you end up facing between NNW and N (closest to north-northwest (NNW)).
342° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 18° |
| Radians | 19π/10 ≈ 5.969026 |
| Gradians | 380 grad |
| Fraction of a turn | 19/20 (95%) |
| Degrees, minutes, seconds | 342° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north-northwest (NNW)) |
Trigonometric values of 342°
| Function | Value |
|---|---|
| sin 342° | −(√5 − 1)/4 ≈ −0.309017 |
| cos 342° | √(10 + 2√5)/4 ≈ 0.951057 |
| tan 342° | −0.32492 |
342° on a protractor
How to draw a 342° angle with a protractor
- Subtract from 360°: 360° − 342° = 18°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 18°.
- Join the vertex to the dot. The inside angle is 18°; the outside angle, going the long way around, is 342°. Draw the angle arc on the outside and label it 342°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 342° directly.
Drawing it a 342° angle without a protractor (rise and run method)
- 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 3.25 inches (about 3 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 18°, because tan 18° ≈ 0.3249.
- That gives you 18°. The outside (reflex) angle is 342°.
Where you see 342° angles
- The Earth turns 342° on its axis in about 22 h 48 min.
- A 342° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
342° angle FAQ
What type of angle is 342°?
A 342° angle is a reflex angle, because it is between 180° and 360°.
Does a 342° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 342° is already larger than both. What it does have is an explement (conjugate) of 18°, the angle that completes a full 360° circle.
How many radians is 342 degrees?
342° = 19π/10 radians ≈ 5.969 rad. To convert degrees to radians, multiply by π/180: 342 × π/180 = 19π/10.
How do I measure a 342° angle on my screen?
Open the online protractor with 342° preset, or type 342 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
