Internal Angle of Equilateral Triangle

Theorem

The internal angles of an equilateral triangle measure $60^\circ$ or $\dfrac \pi 3$ radians.

Proof

By definition, an equilateral triangle is a regular polygon with $3$ sides.

From Internal Angles of Regular Polygon, the size $A$ of each internal angle of a regular $n$-gon is given by:

$A = \dfrac {\paren {n - 2} 180^\circ} n$

Thus:

$A = \dfrac {180^\circ} n = 60^\circ$

From Value of Degree in Radians:

$1^\circ = \dfrac {\pi} {180^\circ} \mathrm {rad}$

and so:

$A = 60^\circ \times \dfrac {\pi} {180^\circ} = \dfrac \pi 3 \mathrm {rad}$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $60$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $60$