 | Hippolyte Taine - Knowledge - 1871 - 606 pages
...the polygon ; so that the angles of the polygon, if we add to them the angles at the vertices, are equal to twice as many right angles as the polygon has sides. Now we know independently that the angles at the vertices are together equal to four right angles ;... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...is equal to two right angles (33) ; therefore the sum of the angles of all the triangles, that is, the sum of the interior angles of the polygon, is...as many right angles as the polygon has sides minus two. PRACTICAL QUESTIONS. 1. Do two lines that do not meet form an angle with each other ? Two lines... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...is equal to two right angles (33) ; therefore the sum of the angles of all the triangles, that is, the sum of the interior angles of the polygon, is...as many right angles as the polygon has sides minus two. PRACTICAL QUESTIONS. 1. Do two lines that do not meet form an angle with each other ? Two lines... | |
 | Edward Olney - 1872 - 270 pages
...at least one re-entrant angle. PROPOSITION XV. 253. 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. Fio. 187. DEM.—Let n be the number of sides of any polygon; then the sum... | |
 | William Frothingham Bradbury - Geometry - 1872 - 88 pages
...-\- b = two right angles (7), and so of he angles at C, D, Д &c. ; .-. the sum of the angles of the of the polygon is equal to twice as many right angles as the figure has sides, lacking four right angles ; .-. a -\- b -\- с -\- d -f-/ = four right angles. 95... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the polygon. The sum of the angles of each triangle is two right angles. Therefore, the sum of the angles of the polygon is equal to twice as many right angles as it has sides, less two. The remark in Article 346 applies as well to this theorem. 434. Let R represent... | |
 | André Darré - 1872 - 226 pages
...polygon ABCDE (Fig. 62) to the vertices of the angles form as many triangles as the figure has sides. The sum of the interior angles of the polygon is equal to the sum of the angles of all the triangles less the sum of the angles formed at the point 0 ; that... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...re.entrant angle. FIG. 186. PROPOSITION XT. 253. Theorem. — The sum of the inferior angles of a polygon s* equal to twice as many right angles as the polygon has sides, less four right angles. DEM. — Let n be the number of sides of any polygon; then the sum of its angles... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...they be similar. For, the corresponding angles in each are equal, because any angle in F( >C either polygon is equal to twice as many right angles as the polygon has sides, less four right angles, divided by the number of angles (B. I, P. XXVI , C. 4); and further, the corresponding... | |
 | Edward Atkins - 1874 - 428 pages
...circle, the sum of the angles in the segments exterior to the polygon, together with two right angles, is equal to twice as many right angles as the polygon has sides. 20. Draw the common tangents to two given circles. 21. From a given point draw a straight line cutting... | |
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The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles. 
