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" The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 15
by George Roberts Perkins - 1860 - 443 pages
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...equal, each to each. PROPOSITION XV. 264. Theorem. — The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. DEMONSTRATION. Let n be the number of aides of any polygon. We are to prove...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...complementary. THEOR. 26. All the interior angles of any convex polygon together with four right angles are equal to twice as many right angles as the polygon has sides. THEOR. 27. The exterior angles of any convex polygon made by producing the sides in order are together...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...equal to two right angles, /. 2. therefore all the interior and all the exterior angles are together equal to twice as many right angles as the polygon has sides ; but the interior angles and four right angles are together equal to twice as many right angles as...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...any convex polygon : A then shall all the interior angles of ABCDE together with four right angles be equal to twice as many right angles as the polygon has sides. Take any point O within the polygon ABCDE, and join O to each of the angular points of the polygon....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...they are similar. For, the corresponding angles in each are equal, because any angle in either polygon is equal to twice as many right angles as the polygon has sides, less four right angles, divided PROPOSITION II. THEOREM. The circumference of a circle may be circumscribed...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...at any one vertex is two right angles (§ 31). Hence the sum of all the interior and exterior angles is equal to twice as many right angles as the polygon has sides. But the sum of the interior angles alone is equal to twice as many right angles as the polygon has...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1886 - 352 pages
...as there are sides of the polygon : hence, the sum of all the interior and exterior angles will be equal to twice as many right angles as the polygon has sides. But the sum of all the interior angles together with four right angles, is equal to twice as many right...
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The Colliery Engineer Pocket-book of Principles Rules, Formulę, and Tables ...

Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...of the exterior angles will equal four right angles. 16. The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles. EXAMPLES. The sum of the interior angles of a quadrilateral = (2X4)— 4 =...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...angles. Let AD represent any convex polygon. To prove that the sum oj the interior angles of the polygon is equal to twice as many right angles as the polygon has sides, minus jour right angles. Suggestion i. Connect each vertex with O, any point within the polygon. 2....
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A Treatise on Mine-surveying

Bennett Hooper Brough - Mine surveying - 1894 - 390 pages
...included angle between the two lines. The sum of the included angles should, with four right angles, be equal to twice as many right angles as the polygon has sides. Station-Line. Distance. Magnetic Bearing. Inclination, Descending. Clmins. Shaft to A 4-58 98° 25'...
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