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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 17
by George Roberts Perkins - 1856 - 235 pages

New Series of The Mathematical Repository, Volume 3

Thomas Leybourn - Mathematics - 1814 - 420 pages
...Hence, by adopting the notation in the question, we have But the sum of the angles of any polygon being equal to twice as many right angles as the polygon has sides, less four; the sum of all the angles of the polygon will be equal to an even number of right angles,...

Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...to say, the sum of the angles of the polygon, together with those about the point within . it, are equal to twice as many right angles as the polygon has sides ; but those angles which are' about the point, amount to four right angles, (Prop. VI. Cor. 2.) deducting...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...figure has sides, wanting four right angles. Hence, the interior angles plus four right .. -i angles, is equal to twice as many right angles as the polygon has aides, and consequently, equal to the sum of the interior angles plus the exterior angles. Taking from...

Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...of each as there arc sides of the polygon ; hence, the sum of all the interior and exterior angles is equal to twice as many right angles as the polygon has sides. Again, the sum of all the interior angles is equal to two right angles, taken as many times, less two,...

Plane Trigonometry and Mensuration for the Use of the Royal Military College

William Scott - Measurement - 1845 - 288 pages
...end ought to coincide. Also, the sum of all the angles, together with four right angles, ought to be equal to twice as many right angles as the polygon has sides (Eue. i. 32. cor.). To find the angle contained by two straight lines conceived to be drawn from a...

Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...of all the interior angles of the polygon formed by joining the stations by straight lines will be equal to twice as many right angles as the polygon has sides, wanting 4 right angles (Euc. Cor. 32, I.) Thus, if the figure have 3 sides, the sum of the interior angles...

Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...(Prop. i) ; •therefore the sum of all the interior angles, together with all the exterior angles, is equal to twice as many right angles as the polygon has sides ; but the sum of all the exterior angles is equal to four right angles (Prop. xxm) ; therefore the...

Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...of each as there are sides of the polygon : hence, the sum of all the interior and exterior angles is equal to twice as many right angles as the polygon has sides. Again, the sum of all tho interior angles is equal to two right angles, taken as many times, less two,...