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Revision difference : supplementary angles |
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| Two angles are called {\em supplementary angles}\, of each other if the sum of their \PMlinkname{measures}{AngleMeasure} is equal to the straight angle $\pi$, \PMlinkname{i.e.}{Ie} $180^\circ$.\\ |
Two angles are called {\em supplementary angles}\, of each other, if their sum is equal to the straight angle $\pi$, i.e. $180^\circ$. |
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| For example, when two lines intersect each other, they \PMlinkescapetext{divide} the plane into four disjoint \PMlinkname{domains}{Domain2} corresponding to four convex angles; then any of these angles has a supplementary angle on either side of it (see linear pair). However, two angles that are supplementary to each other do not need to have a common side --- see \PMlinkname{e.g.}{Eg} an entry regarding \PMlinkname{opposing angles in a cyclic quadrilateral}{OpposingAnglesInACyclicQuadrilateralAreSupplementary}.\\ |
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| Supplementary angles have always equal sines, but the cosines are opposite numbers: |
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| $$\sin(\pi\!-\!\alpha) \;=\; \sin\alpha, \qquad \cos(\pi\!-\!\alpha) \;=\; -\cos\alpha$$ |
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| These formulae may be proved by using the subtraction formulas of sine and cosine. |
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For example, when two lines intersect each other, they divide the plane into four disjoint domains corresponding four convex angles; then any of these angles has on its both sides its supplementary angle (see linear pair). However, an angle and its supplementary angle do not need to have a common side --- see e.g. \PMlinkname{this entry}{OpposingAnglesInACyclicQuadrilateralAreSupplementary}. |
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