Angle — 45° (Acute Angle) — free printable diagram

What is a 45 degree angle?

A 45 degree angle (45°) is an acute angle — it measures less than 90°, so the opening is narrower than a square corner. This diagram shows 45° opened between two arms meeting at a vertex.

Measure

45°

Type of angle

Acute angle

Complement (adds to 90°)

45°

Supplement (adds to 180°)

135°

Reflex angle on the other side

315°

In radians

π/4 (≈0.785)

Fraction of a full turn

1/8 of a turn

Exterior angle of

a regular octagon

• A 45° 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° − 45° = 135°.
• Two angles that add up to 90° are complementary, so the complement of 45° is 90° − 45° = 45°.
• Angles round a point add up to 360°, so the reflex angle on the other side of these arms measures 360° − 45° = 315°.
• 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 45°.
• In radians, 45° × π/180 = π/4, which is about 0.785.
• Turning 45° at each corner brings you all the way round after 8 turns, which is why 45° is the exterior angle of a regular octagon.