...angles. OüTUSE-ütOLSD, Having one obtuse angle, and, of necessity, twoacuteangles. Now, as the three interior angles of a triangle are together equal to two right angles or 180 degrees, and as an obtuse angle is any angle greater than a right angle or 90 degrees, while...

...THEOR. * • > An exterior angle of a triangle is equal to both its opposite interior angles, and all the interior angles of a triangle are together equal to two right angles. The exterior angle BCD, formed by the production of the side AC of the triangle ABC, is equal to the...

...of the arc which measures the angle А С В, will be equal to the radius of the circle. For as all the interior angles of a triangle are, together, equal to two right angles, (Theo. 24.) if А С В be the third part of two right angles, the remaining angles A and B will, together,...

...reasoning will clearly apply to every triangle of which one side (AD) is produced. Cor. 2. — The three interior angles of a triangle are together equal to two right angles. This follows, as in Euclid's 32nd. If, however, it be said that it is premature to state that the angles...

...by the number of units of length they respectively contain ; for otherwise sin Л and a would not be quantities of the same kind, and consequently no ratio...a triangle are together equal to two right angles, we have A + B+C=180°. sin A a Also ; -r— = - , sin В о sin B b sin C с And if three of the parts...

...most remarkable propositions in the whole book, namely, the 32d, in which it is shown that the three interior angles of a triangle are together equal to two right angles. This important fact has already been examined, and therefore we have only to add that it was discovered...

...Euclid. THEOREM. An exterior angle of a triangle is equal to both its opposite interior angles, and all the interior angles of a triangle are together equal to two right angles. The exterior angle BCD formed by the production of the side AC of the triangle ABC, is equal to the...

...right angles, or the lines PQ, QR would not meet. This follows also from the theorem that the three interior angles of a triangle are together equal to two right angles. PROBLEM 7. Having given two angles and a side opposite to one of them, to construct the triangle. V...

...ABC; that is, ACD, which is made up of ACE and EC D, is equal to BAC and AB C. 127. PROP. The three interior angles of a triangle are together equal to two right angles (fig. No. 126). By the above proposition, ACD is equal to the sum of ABC and BAC. Add to each ACB;...

...produced, the exterior angle is equal to the sum of the two interior and opposite angles; and the three interior angles of a triangle are together equal to two right angles. For the construction employed in this proposition we must be able to draw through a given point a right...