Definition:Obtuse Angle

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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:

$90^\circ < \theta < 180^\circ$

or:

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