Measurements of Common Angles/Straight Angle
Theorem
The measurement of a straight angle is $180 \degrees$ or $\pi$ radians.
Proof
From Measurement of Full Angle, a full rotation is defined to be $360 \degrees$ 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:
- $\dfrac {360 \degrees} 2 = 180 \degrees$
or:
- $\dfrac {2 \pi} 2 = \pi$
$\blacksquare$
Also see
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $180$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $180$
- 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): angular measure
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): flat angle (straight angle)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): straight angle (flat 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): angular measure
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): flat angle (straight angle)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): straight angle (flat angle)