Angle — 40° (Acute Angle) — free printable diagram

What is a 40 degree angle?

A 40 degree angle (40°) is an acute angle — it measures less than 90°, so the opening is narrower than a square corner. This diagram shows 40° opened between two arms meeting at a vertex.

Measure

40°

Type of angle

Acute angle

Complement (adds to 90°)

50°

Supplement (adds to 180°)

140°

Reflex angle on the other side

320°

In radians

2π/9 (≈0.698)

Fraction of a full turn

1/9 of a turn

Exterior angle of

a regular nonagon

• A 40° angle is an acute angle because it measures less than 90°, so the opening is narrower than a square corner.
• Angles on a straight line add up to 180°, so the angle next to this one measures 180° − 40° = 140°.
• Two angles that add up to 90° are complementary, so the complement of 40° is 90° − 40° = 50°.
• Angles round a point add up to 360°, so the reflex angle on the other side of these arms measures 360° − 40° = 320°.
• To measure or draw it, put the centre of the protractor on the vertex where the two arms meet, line one arm up with the 0° mark, and read the scale that starts at 0° on that arm until you reach 40°.
• In radians, 40° × π/180 = 2π/9, which is about 0.698.
• Turning 40° at each corner brings you all the way round after 9 turns, which is why 40° is the exterior angle of a regular nonagon.