 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...... Th. XXIV. Therefore, if, etc. QUERY. THEOREM XXVI. The sum of the interior angles of a polygon, plus four right angles, is equal to twice as many right angles as the polygon has sides. For, take any polygon, as ABCD E. If from any point within it, as F, lines be drawn to the vertices... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 1885 - 608 pages
...straight line. 4. Show that the sum of the interior angles of any rectilineal figure together witli four right angles, is equal to twice as many right angles as the figure has sides. 5. Prove that the opposite sides and angles of a parallelogram are equal to one another,... | |
 | 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... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...formed 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... | |
 | 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... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...are equal to two right angles : that the sum of the angles of any rectilineal figure together with four right angles is equal to twice as many right angles as the figure has sides : and that the sum of the distances of any point from the angular points of the figure... | |
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Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles. 
