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- ..., we may use a method that can be called "perturbation". If we let all the angles <math>A,B,C</math> be equal, we prove that if we make one angle greater and ...th> is cyclic, we have that <math>B</math> and <math>\angle FPD</math> are supplementary. Since <math>MPD</math> is a line, <math>B = \angle FPM.</math> This means7 KB (1,300 words) - 00:11, 28 October 2024
- * Consecutive angles are [[supplementary]].910 bytes (122 words) - 20:48, 13 November 2024
- * 2 pairs of congruent [[angles]] * opposite angles are supplementary577 bytes (81 words) - 09:33, 18 April 2019
- ...nd <math>PBM</math> are congruent. Since these angles are [[supplementary angles]], each of them must be a [[right angle]]. Hence <math>PM</math> is the pe2 KB (367 words) - 14:20, 1 January 2014
- ...]] it is most commonly used in [[geometry]]: two [[angle]]s are said to be supplementary if they sum to <math>\displaystyle \pi</math> [[radian]]s (180 [[degree (g263 bytes (39 words) - 10:02, 7 September 2006
- There are many [[notation]]s for angles. The most common form is <math>\angle ABC</math>, read "angle ABC", where < ...ath>, read "measure of angle ABC". There are different units for measuring angles. The three most common are [[degree (geometry) | degrees]], [[radian]]s an4 KB (597 words) - 17:39, 9 May 2024
- ...ws from the fact that the angles <math>AMC</math> and <math>CMB</math> are supplementary. replacing some angles, we get4 KB (740 words) - 17:03, 14 November 2024
- ...math>\angle ADB</math> are equal (this also holds for three other pairs of angles, found by considering equivalent quadrilaterals <math>BCDA</math>, <math>CD ...le CDA</math> are [[supplementary]] (this also holds for the other pair of angles <math>\angle BCD</math> and <math>\angle DAB</math>.2 KB (291 words) - 04:30, 16 August 2011
- ...such that diagonals <math>AC</math> and <math>BD</math> intersect at right angles, and let <math>E</math> be their intersection. Prove that the reflections o Thus, <math>\angle XYZ</math> and <math>\angle XWZ</math> are supplementary and follows that, <math>XYZW</math> is cyclic.4 KB (679 words) - 04:42, 1 October 2024
- ...quadrilateral. As a property of cyclic quadrilaterals, opposite angles are supplementary so <math>\angle BAD = 180 - \angle BCD</math>, therefore <math>\cos{\angle2 KB (262 words) - 15:43, 15 February 2021
- ...<math>\overline{AB}</math> is parallel to <math>\overline{ED}</math>. The angles <math>AEB</math> and <math>ABE</math> are in the ratio <math>4 : 5</math>. ...\overline{ED}</math>. Opposite angles in a [[cyclic]] quadrilateral are [[supplementary]], so <math>\angle BED + \angle BCD = 180</math>. Use substitution to get <5 KB (699 words) - 03:53, 21 January 2023
- ...(180^{\circ} - \theta)}, </math> as two angles along the same line must be supplementary. This simplifies to <math> \sin{\theta} + \sin{(180^{\circ} - \theta)} = \f2 KB (379 words) - 00:59, 16 February 2021
- ...X =\text{arc}\ OY \implies \angle{OZY} \cong \angle{OZX}</math>, since the angles inscribe arcs of the same length. ...Z}</math>. Since <math>\angle{OYZ}</math> and <math>\angle{OXZ}</math> are supplementary, <math>\angle{OXZ}=\pi-\theta</math>. Using the law of cosines on <math>\tr9 KB (1,496 words) - 19:13, 21 September 2024
- Since angles <math>\angle AB'P</math> and <math>\angle CB'P</math> are supplementary or equal, depending on the position of <math>B'</math> on <math>AC</math>, ...ective property, <math>\angle APB'</math> and <math>\angle BPA'</math> are supplementary or equal, so5 KB (767 words) - 21:32, 2 May 2023
- ...and <math>DCE</math>, and let <math>S'</math> represent the degree-sum of angles <math>BAD</math> and <math>ABC.</math> If <math>r=S/S'</math>, then: ...math>\angle DCE</math> and <math>\angle CDE</math>, respectively, the four angles sum to <math>2*180^{\circ}=360^{\circ}</math>, so <math>\measuredangle BCD+2 KB (284 words) - 18:06, 17 July 2024
- The measures of the interior angles of a convex polygon are in arithmetic progression. \textbf{II. }\angle ACB \text{ and }\angle DFE\text{ must be supplementary.}\17 KB (2,835 words) - 13:36, 8 September 2021
- ...les in triangle <math>ABC</math> is <math>180^\circ</math> and we know two angles <math>93^\circ</math> and <math>50^\circ</math> which add to <math>143^\cir1 KB (158 words) - 00:46, 23 October 2014
- ...ngles are simply the angles of triangle <math>S</math>; out of these three angles, <math>\alpha</math> is the smallest angle, and <math>\theta</math> is the ...rilaterals). Since <math>\angle PAX</math> and <math>\angle PAZ</math> are supplementary, <math>Z</math>, <math>A</math>, and <math>X</math> are collinear as desire22 KB (3,622 words) - 21:06, 10 October 2024
- ..., <math>BE=b</math>. Because opposite angles in a cyclic quadrilateral are supplementary, we have <math>\angle EMI=90^{\circ}</math>. By the law of cosines, we have7 KB (1,218 words) - 03:03, 23 January 2023
- .../math> represent the same angle or the two numbers represent supplementary angles. In the first case there is an integer <math>k</math> such that <math>720\t7 KB (1,211 words) - 23:23, 19 January 2024