Measurements of Common Angles/Straight Angle

Theorem

The measurement of a straight angle is $\dfrac{360^\circ} 2 = 180^\circ$ or $\dfrac {2 \pi} 2 = \pi$.

Proof

From $2 \pi$ radians, a full rotation is defined to be $360^\circ$ or $2 \pi$ radians.

Since lines are straight, it therefore follows that from any point on a line, the angle between one side of the line and the other is one half of a full rotation.

Therefore, the measurement of a straight angle is:

$\dfrac{360^\circ} 2 = 180^\circ$

or:

$\dfrac {2 \pi} 2 = \pi$

$\blacksquare$

Also see

• Two Angles making Two Right Angles make Straight Line

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $180$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $180$