A 135° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 45°, so a 135° angle and a 45° angle side by side make a straight line.
135° is 3/8 of a full circle, or 3π/4 radians. If you face north and turn 135° clockwise, you end up facing due southeast (SE).
135° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 45° |
| Explement (adds to 360°) | 225° |
| Radians | 3π/4 ≈ 2.356194 |
| Gradians | 150 grad |
| Fraction of a turn | 3/8 (37.5%) |
| Degrees, minutes, seconds | 135° 0′ 0″ |
| Compass bearing | southeast (SE) |
Trigonometric values of 135°
| Function | Value |
|---|---|
| sin 135° | √2/2 ≈ 0.707107 |
| cos 135° | −√2/2 ≈ −0.707107 |
| tan 135° | −1 |
135° on a protractor
How to draw a 135° 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 135° 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 135°.
Drawing it a 135° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 45° angle: construct a 90° angle, then bisect it.
- What is left between the first arm and the new line is 180° − 45° = 135°.
Where you see 135° angles
- Each corner of a stop sign (a regular octagon) is 135°.
- Baseball's home plate has two 135° corners.
- At 1:30 the hands of a clock are 135° apart.
- Split-drill-point bits for hard metals use a 135° point angle.
- Each interior corner of a regular octagon measures 135°.
- The Earth turns 135° on its axis in about 9 hours.
Related angles
135° angle FAQ
What type of angle is 135°?
A 135° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 135°?
The supplement of 135° is 45°, because 135° + 45° = 180°. A 135° angle has no complement, because it is already larger than 90°.
How many radians is 135 degrees?
135° = 3π/4 radians ≈ 2.3562 rad. To convert degrees to radians, multiply by π/180: 135 × π/180 = 3π/4.
How do I measure a 135° angle on my screen?
Open the online protractor with 135° preset, or type 135 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.