Definition:Obtuse Angle

Definition

An obtuse angle is an angle which has a measurement between those of a right angle and a straight angle.

In the words of Euclid:

An obtuse angle is an angle greater than a right angle.

(The Elements: Book $\text{I}$: Definition $11$)

Note that Euclid did not consider the concept of reflex angles.

Measurement of Obtuse Angle

An obtuse angle measures $\theta$, where:

$90 \degrees < \theta < 180 \degrees$

or:

$\dfrac \pi 2 < \theta < \pi$

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): obtuse: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angle
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): obtuse angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): obtuse angle
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): obtuse angle