Measurements of Common Angles/Acute Angle

Theorem

An acute angle measures $\theta$, where:

$0 \degrees < \theta < 90 \degrees$

or:

$0 < \theta < \dfrac \pi 2$

Proof

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

A zero angle measures $0$ by definition, and a right angle measures $90 \degrees$ or $\dfrac \pi 2$.

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angle