explementaryExplementary2007-10-11 07:35:312009-06-04 13:52:10Definitionangleexplementary angleexplementary arcfull angle% this is the default PlanetMath preamble. as your knowledge
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The {\em explementary arc} of an arc $a$ of a circle is the arc forming together with $a$ the full circle.
Two angles are called {\em explementary angles} of each other, if their sum is the {\em full angle} $2\pi$, i.e. $360^\circ$. In the below picture, the \PMlinkescapetext{interior angle} \,$\alpha = 60^\circ$\, of an equilateral triangle and its explementary angle\, $\beta = 300^\circ$\, (which is an \PMlinkescapetext{exterior angle} of the triangle) are seen.
\begin{center}
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\pspolygon(-1.5,0)(1.5,0)(0,2.6)
\psarc(0,2.6){0.2}{-60}{240}
\rput[a](0,2.2){$\alpha$}
\rput[a](-0.2,2.9){$\beta$}
\rput(-2,-0.5){.}
\rput(2,3){.}
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