...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, and that the...

...straight line. 2. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. If...

...angles is expressed by 2 R x (n — 2) , or 2 nR — 4 R. That is, the sum of the angles of a polygon is equal to twice as many right angles as the figure, has sides, less four right angles. PROPOSITION XLVII. THEOREM. 149. If the sides of a polygon are produced so as to form an exterior angle...

...every station on a survey. In any polygon, regular or irregular, the sum of all the interior angles is equal to twice as many right angles as the figure has sides, less four right angles. As observed above, and as may be seen by referring to the figure 52, whether we consider the regular...

...produced to meet, the angles formed by these lines, together with eight right angles, are together equal to twice as many right angles as the figure has sides. 139. AP, BP, and CP are the internal bisectors of the angles of the triangle ABC. AP is produced to...

...accuracy of the survey, as the interior angles of the polygon together with four right angles should be equal to twice as many right angles as the figure has sides. The interior angles of a traverse may be found from the bearings or courses by the following rules...

...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 is greater than...

...2 rt. Zs (n — 2) = 2n rt. Zs — 4 rt. Zs. Therefore, the sum of the angles of a polygon is also equal to twice as many right angles as the figure has sides, less four right angles. 149. COR. 2. The sum of the angles of a quadrilateral is equal to two right angles taken (4 — 2)...

...case of a particular polygon that the sum of its interior angles, together with four right angles, is equal to twice as many right angles as the figure has sides — and conclude that the law holds good of all polygons. In calculating the terms of a ' Mill's Logic,...

...63. THEOE. 6. All the interior angles of any rectilinieal figure together with four right angles, are equal to twice as many right angles as the figure has sides (Euc. I. 32. Cor. 1). Hence the angles of a regular polygon are each equal to the quotient obtained...