Measurements of Common Angles/Obtuse Angle

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An obtuse angle measures $\theta$, where:

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


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


An obtuse angle is defined to be an angle whose measure is between that of a right angle and a straight angle.

A right angle measures $90^\circ$ or $\dfrac \pi 2$ and a straight angle measures $180^\circ$ or $\pi$.

Hence the result.