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• Conic section
  ...described in [[Cartesian coordinates]] by a [[polynomial]] [[equation]] of degree two or less. ...cutting plane makes an [[angle]] with an [[axis]] that is larger than the angle between the slant height and the axis.
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• Geometry
  ...he intersection two [[ray]]s at their endpoints. It is measure in either [[degree]]s or [[radian]]s, though the less-common [[Système international|metric]]
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• 2002 AMC 12A Problems
  Find the degree measure of an angle whose complement is 25% of its supplement. ...a right triangle with <math>\angle ACB</math> as its right angle, <math>m\angle ABC = 60^{\circ}</math>, and <math>AB = 10</math>. Let <math>P</math> be ra
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• 2001 AMC 12 Problems
  ...1,4)</math>, and <math>E=(0,4)</math>. What is the probability that <math>\angle APB</math> is obtuse? A polynomial of degree four with leading coefficient 1 and integer coefficients has two real zeros
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• 2002 AMC 12B Problems
  Let <math>v, w, x, y, </math> and <math>z</math> be the degree measures of the five angles of a pentagon. Suppose that <math>v < w < x < y Let <math>\triangle XOY</math> be a right-angled triangle with <math>\angle XOY = 90^{\circ}</math>. Let <math>M</math> and <math>N</math> be the midpo
  10 KB (1,547 words) - 04:20, 9 October 2022
• 2006 AMC 12A Problems/Problem 22
  ...probability of choosing a point is <math>1 / 2</math>, or if the total arc degree measures add up to <math>\frac{1}{2} \cdot 360^{\circ} = 180^{\circ}</math> ...an [[isosceles triangle]]: <math>\angle AOP = 15^{\circ}</math> and <math>\angle OAP = OAB - 60^{\circ} = \frac{180^{\circ}-30^{\circ}}{2} - 60^{\circ} = 15
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• 2006 AMC 10A Problems/Problem 19
  How many non-[[similar]] triangles have angles whose degree measures are distinct positive integers in [[arithmetic progression]]? ...c{180}{3} = 60</math> degrees. The minimum possible value for the smallest angle is <math>1</math> and the highest possible is <math>59</math> (since the nu
  2 KB (259 words) - 03:10, 22 June 2023
• 2005 AIME II Problems/Problem 12
  ...E<BF </math> and <math> E </math> between <math> A </math> and <math> F, m\angle EOF =45^\circ, </math> and <math> EF=400. </math> Given that <math> BF=p+q\ ...math>). Then <math>\tan \angle EOG = \frac{x}{450}</math>, and <math>\tan \angle FOG = \frac{y}{450}</math>.
  13 KB (2,080 words) - 21:20, 11 December 2022
• 2004 AIME II Problems/Problem 1
  ...angle]] which contains the entire chord is <math>60 \cdot 2 = 120</math> [[degree]]s, so the area of the [[sector]] is <math>\frac{1}{3}r^2\pi</math>; the re
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• 1984 AIME Problems
  ...circ</math> and <math>180^\circ</math> in the complex plane. Determine the degree measure of <math>\theta</math>. ...{ cm}^2</math>. These two faces meet each other at a <math>30^\circ</math> angle. Find the volume of the tetrahedron in <math>\mbox{cm}^3</math>.
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• 2001 AIME I Problems
  ...</math> degrees and <math>45</math> degrees, respectively. The bisector of angle <math>A</math> intersects <math>\overline{BC}</math> at <math>T</math>, and ...where <math>d < 120.</math> The length of the chord of a <math>3d</math>-degree arc is <math>- m + \sqrt {n}</math> centimeters, where <math>m</math> and <
  7 KB (1,212 words) - 22:16, 17 December 2023
• 1983 AIME Problems/Problem 14
  ...must add up to <math>180^{\circ}</math>. By the [[Law of Cosines]], <math>\angle APB=\cos^{-1}\left(\frac{{-11}}{24}\right)</math>. Also, angles <math>QPA</ ...). In other words, since <math>\angle TP'N = 90^\circ</math>, then <math> \angle TPN = 90^\circ</math>.
  13 KB (2,149 words) - 18:44, 5 February 2024
• 2001 AIME I Problems/Problem 13
  ...where <math>d < 120.</math> The length of the chord of a <math>3d</math>-degree arc is <math>- m + \sqrt {n}</math> centimeters, where <math>m</math> and < ...of the chords, <math>AD</math> and <math>BC</math>, of the <math>2d</math>-degree arcs can be represented as <math>x + 20</math>, as given in the problem.
  3 KB (561 words) - 19:25, 27 November 2022
• 2000 AIME II Problems/Problem 15
  ...in(1)=\frac{1}{60}</math> in degrees, convert to radians and use the small angle approximation <math>\sin(x)=x</math>. Hence, <math>S=\sin(1)</math>, and our angle is <math>\boxed{001}</math>.
  3 KB (469 words) - 21:14, 7 July 2022
• 1959 IMO Problems/Problem 4
  ...> is <math>ab</math>, since <math>a</math> and <math>b</math> form a right angle. However, twice the area of the triangle is also the product of <math>c</m We denote the angle between <math>b</math> and <math>c</math> as <math>\alpha</math>. The prob
  6 KB (939 words) - 17:31, 15 July 2023
• Right angle
  ...ne]]s. The [[measure of an angle | measure]] of every right angle is 90 [[degree (geometry) | degrees]] or <math>\frac \pi 2</math> [[radian]]s. When drawin * [[Angle]]
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• Supplementary
  ...ementary if they sum to <math>\displaystyle \pi</math> [[radian]]s (180 [[degree (geometry) | degrees]]).
  263 bytes (39 words) - 11:02, 7 September 2006
• Angle
  ...ex]] of the angle, and the rays themselves are called the [[side]]s of the angle. ...If there is no ambiguity, this notation can be shortened to simply <math>\angle B</math>.
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• Radian
  ...measurement for [[angle|angles]]. In a circle, the measure of a [[central angle]] in radians is the ratio of the length of the [[intercepted arc]] to the l ...the whole circumference of the circle. Thus, radians can be converted to [[Degree (geometry)|degrees]]: <math>2\pi\; rad=360^\circ\implies\pi \;rad=180^\circ
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• Degree
  * [[Degree (geometry)]], the degrees in an [[angle]]. * [[Degree (graph theory)]], the degree of a [[vertex]] in a [[graph (graph theory) | graph]].
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• Hexagon
  ...ternal [[angle]] of a [[Regular polygon | regular]] hexagon measures 120 [[degree (geometry) | degrees]], so the sum of the angles is <math>720^{\circ}</math
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• Straight angle
  ...ting in opposite directions. The measure of every straight angle is 180 [[degree (geometry) | degrees]] or <math>\pi</math> [[radian]]s. * [[Angle]]
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• Obtuse angle
  An '''obtuse angle''' is an [[angle]] with a [[measure]] greater than 90 [[degree (geometry) | degrees]] (<math>\frac\pi2</math> [[radian]]s) but less than 1 Any triangle with an obtuse angle is considered an [[Obtuse Triangle]]
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• Acute angle
  ...ngle''' is an [[angle]] with [[measure]] greater than 0 but less than 90 [[degree (geometry) | degrees]] (<math>\frac\pi2</math> [[radian]]s). Examples:http://www.google.com/search?q=acute+angle&hl=en&client=safari&rls=en&prmd=imvns&tbm=isch&tbo=u&source=univ&sa=X&ei=vp
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• Measure
  ...'measure''' can mean the amount of [[degree (geometry) | degree]]s in an [[angle]], the [[length]] of a [[line segment]], or a [[function]] that assigns a [ ...h>\angle ABC\cong\angle DEF</math>, then <math>\mbox{m}\angle ABC=\mbox{m}\angle DEF</math>.
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• Degree (geometry)
  The '''degree''' of an [[angle]] is a [[measure]]ment of the angle, representing <math>\frac1{360}</math> of a full [[rotation]]. Degrees are indicated by the degree symbol; one degree would be written <math>1^{\circ}</math>.
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• Point
  ...angle]] can be denoted by either one or three points. If there is only one angle with this point as its [[vertex]], only one point is needed; if there are m ...y either two or three points. If the arc has a [[measure]] less than 180 [[degree]]s, only two points are needed; if the arc has a measure equal to or greate
  3 KB (461 words) - 18:59, 22 April 2008
• Mock AIME 6 Pre 2005/Problems
  <math>13</math>. In <math>\triangle ABC</math>, <math>\angle A=30^{\circ}</math>, <math>AC=28\sqrt{3}</math>, and <math>\displaystyle AB <math>14</math>. Let <math>\displaystyle f</math> be a polynomial of degree <math>\displaystyle 2005</math> with leading coefficient <math>\displaystyl
  7 KB (1,110 words) - 05:15, 31 December 2006
• 2007 AIME II Problems/Problem 11
  ...r circle (twice), while the <math>180 - 2(30) = 120^{\circ}</math> central angle in the smaller circle indicates to take <math>\frac{120}{360} = \frac 13</m
  2 KB (407 words) - 16:31, 29 February 2020
• 2007 AMC 12A Problems
  ...angle <math>ADC</math> measures 140 degrees. What is the degree measure of angle <math>BAD</math>? ...10 to 3, and so on, ending back at 12. What is the degree measure of the [[angle]] at each [[vertex]] in the star polygon?
  11 KB (1,750 words) - 13:35, 15 April 2022
• 2007 AMC 12B Problems/Problem 3
  ...e AOB = 140^{\circ}</math>, as shown. What is the degree measure of <math>\angle ABC</math>? ...\angle ABO=20^o</math> and <math>\angle OBC=30^o</math>. Therefore, <math>\angle ABC=50^o</math>, or <math>\mathrm{(D)}</math>.
  905 bytes (130 words) - 10:39, 27 February 2022
• 2007 AMC 12B Problems/Problem 7
  ...gle A = \angle B = 90^{\circ}</math>. What is the degree measure of <math>\angle E</math>? ...also 5, triangle <math>CDE</math> is [[equilateral triangle|equilateral]]. Angle <math>E</math> is therefore <math>90+60=150 \Rightarrow \mathrm {(E)}</math
  860 bytes (126 words) - 18:31, 17 June 2023
• Central angle
  ...entral angle subtends is by definition equal to the measure of the central angle, and is known as the [[arc segment]]'s [[angular distance]]. * [[Degree]]
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• Octagon
  ...ternal [[angle]] of a [[Regular polygon | regular]] octagon measures 135 [[degree (geometry) | degrees]], so the sum of the angles is <math>1080^{\circ}</mat
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• 2007 AMC 12A Problems/Problem 6
  ...angle <math>ADC</math> measures 140 degrees. What is the degree measure of angle <math>BAD</math>? We angle chase and find out that:
  2 KB (265 words) - 00:20, 30 October 2022
• 2007 AMC 12A Problems/Problem 8
  ...10 to 3, and so on, ending back at 12. What is the degree measure of the [[angle]] at each [[vertex]] in the star polygon? ...of the [[right angle]]). Thus, the angle at each vertex is an [[inscribed angle]] subtending <math>60</math> degrees, making the answer <math>\frac 1260 =
  997 bytes (152 words) - 03:00, 20 July 2016
• 2005 AMC 12A Problems/Problem 15
  ...ered pair for <math>D (x,y)</math>, and notice how <math>E</math> is a 180 degree rotation of <math>D</math>, using the rotation matrix formula we get <math> ...sion of <math>DC</math> hits the circle <math>F</math>. Notice that <math>\angle DCB = 90^\circ</math>. This implies that <math>DC=CF</math>. WOLG, let <mat
  14 KB (1,970 words) - 17:02, 18 August 2023
• 2006 AIME II Problems/Problem 1
  ...[right angle]]s, and <math>\angle B, \angle C, \angle E,</math> and <math>\angle F</math> are [[congruent]]. The area of the hexagonal region is <math>2116( Because <math>\angle
  2 KB (336 words) - 03:19, 12 January 2024
• 2007 AMC 12B Problems
  ...e AOB = 140^{\circ}</math>, as shown. What is the degree measure of <math>\angle ABC</math>? ...gle A = \angle B = 90^{\circ}</math>. What is the degree measure of <math>\angle E</math>?
  12 KB (1,814 words) - 12:58, 19 February 2020
• 2002 AMC 12A Problems/Problem 4
  Find the degree measure of an angle whose complement is 25% of its supplement. ...e <math>90^{\circ}</math> as <math>\frac{3}{4}</math> of the supplementary angle.
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• 1999 AHSME Problems
  ...mum number of points of intersection of the graphs of two different fourth degree polynomial functions <math>y = p(x)</math> and <math>y = q(x)</math>, each ...4 \cos B = 6</math> and <math>4 \sin B + 3 \cos A = 1</math>. Then <math>\angle C</math> in degrees is
  13 KB (1,945 words) - 18:28, 19 June 2023
• Reflex angle
  A '''reflex angle''' is an angle whose measure is greater than 180 degrees and less than 360 degrees. |style = "background:#f2f2f2; text-align:center;" | '''[[Degree (geometry)|Degree]]s'''&nbsp;&nbsp;
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• 2007 AMC 10A Problems
  ...angle <math>ADC</math> measures 140 degrees. What is the degree measure of angle <math>BAD</math>? ...des has length <math>4</math>, and each two consecutive sides form a right angle. Suppose that <math>\overline{AG}</math> and <math>\overline{CH}</math> mee
  13 KB (2,058 words) - 17:54, 29 March 2024
• 1966 AHSME Problems
  ...tered at <math>O</math>. <math>C</math> is a point on the circle such that angle <math>BOC</math> is <math>60^\circ</math>. If the diameter of the circle is ...h>BAC</math> are in the ratio <math>2: 3: 4</math>. <math>BD</math> is the angle-bisector drawn to the shortest side <math>AC</math>, dividing it into segme
  19 KB (3,159 words) - 22:10, 11 March 2024
• Three Greek problems of antiquity
  ...then show that <math>x</math> must be an [[algebraic number]] and that the degree of it's [[minimal polynomial]] must be a power of <math>2</math>. ==Trisection of the General Angle==
  2 KB (359 words) - 17:06, 11 June 2022
• 2007 AMC 12B Problems/Problem 14
  .../math> to <math>\overline{BC}</math> be <math>D</math>. Also, since <math>\angle{PQD}=60</math>, let the foot of the altitude from <math>P</math> to <math>\
  3 KB (401 words) - 22:58, 8 May 2023
• 2008 AMC 10B Problems/Problem 24
  ...<math>m\angle BCD = 170^\circ</math>. What is the degree measure of <math>\angle BAD</math>? ...ath>AYB</math> equal to <math>60</math> degrees. We can also find out that angle <math>CYB</math> equals <math>120</math> degrees.
  12 KB (1,944 words) - 17:15, 20 January 2024
• 2008 AMC 10A Problems/Problem 19
  ...RS,\, \angle P'RQ'</math> are complementary, it follows that the arc has a degree measure of <math>90^{\circ}</math> and length <math>\frac14</math> of the [
  2 KB (321 words) - 17:52, 7 November 2021
• 2008 iTest Problems
  Let <math>\triangle XOY</math> be a right-angled triangle with <math>\angle XOY=90^\circ</math>. Let <math>M</math> and <math>N</math> be the midpoints ...C</math> in the sand such that <math>\angle ACB=90^\circ</math> and <math>\angle CBA=15^\circ</math>. He then picks a point at random from within the triang
  71 KB (11,749 words) - 01:31, 2 November 2023
• 2002 AMC 12A Problems/Problem 7
  ...that in a circle with radius <math> r </math>, a subtended arc opposite an angle of <math>\theta</math> degrees has length <math>\frac{\theta}{360} \cdot 2\ ...er based on the choices. Firstly, if a higher angle measure equals a lower angle measure, that means that the ratio of areas must be lower, cutting D and E.
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