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• 2009 AMC 10A Problems/Problem 17
  ...s congruent to <math>DBA</math> and angle <math>ADC</math> is also a right angle. By the transitive property: ...angle has a degree measure of <math>180</math>, angle <math>BEA</math> and angle <math>DBA</math> are similar.
  4 KB (684 words) - 21:14, 23 October 2023
• 2001 AMC 12 Problems/Problem 24
  ...math>2\cdot BD=CD</math> and <math>\angle DAB=15^\circ</math>. Find <math>\angle ACB.</math> ...<math>\triangle{ABH}</math> we get <math>BH=kt</math>. Using the 60-degree angle in <math>\triangle{ADH}</math>, we obtain <math>DH=\frac{\sqrt{3}}{3}kt</ma
  8 KB (1,316 words) - 22:48, 7 March 2024
• 2009 AMC 10B Problems
  ...>\angle A = \frac 52 \angle B</math>. What is the degree measure of <math>\angle D</math>? ...h>, <math>AB=1</math>, and <math>BC=2</math>. The angle bisector of <math>\angle A</math> intersects side <math>\overline{BC}</math> at <math>D</math>. What
  15 KB (2,262 words) - 00:53, 18 June 2021
• 2009 AMC 10B Problems/Problem 9
  ...>\angle A = \frac 52 \angle B</math>. What is the degree measure of <math>\angle D</math>? <math>\triangle ABC</math> is isosceles, hence <math>\angle ACB = \angle CAB</math>.
  2 KB (241 words) - 17:39, 28 June 2021
• 2009 AMC 10B Problems/Problem 24
  ...let <math>x</math> be the angle measure in degrees of the larger interior angle of the trapezoid. What is <math>x</math>? ...\circ}2 = 80^\circ</math>, hence the degree measure of the larger interior angle is <math>180^\circ - 80^\circ = \boxed{100^\circ \Longrightarrow A}</math>.
  3 KB (546 words) - 04:26, 16 January 2023
• 1989 AJHSME Problems/Problem 10
  What is the number of [[degree|degrees]] in the smaller [[angle]] between the hour hand and the minute hand on a clock that reads seven o'c ...clock. A circle is <math>360^\circ</math>, so the measure of the smaller angle is
  683 bytes (100 words) - 23:57, 4 July 2013
• 2003 AMC 12B Problems/Problem 25
  ...m amount of freedom we have to place the third point is a <math>120</math> degree arc(if the first two are the same point), with a <math>\frac{1}{3}</math> p ...degrees, the probability changes linearly (every degree it moves, adds one degree to where the third could be).
  4 KB (635 words) - 11:46, 1 September 2022
• 2010 AMC 12A Problems/Problem 17
  ...ngle{EFA}</math> are congruent by SAS, so the side opposite the 120 degree angle is also the same (since the triangles are congruent). Thus <math>\triangle{
  4 KB (690 words) - 10:13, 14 October 2022
• 2010 AMC 10B Problems
  ...ath> is a diameter and <math>C</math> is a point on the circle with <math>\angle COB = 50^\circ</math>. What is the degree measure of <math>\angle CAB</math>?
  12 KB (1,817 words) - 22:44, 22 December 2020
• 2010 AIME II Problems
  Find the number of second-degree polynomials <math>f(x)</math> with integer coefficients and integer zeros f ...th> on <math>\overline{AB}</math> is chosen such that <math>\angle APC = 2\angle ACP</math> and <math>CP = 1</math>. The ratio <math>\frac{AP}{BP}</math> ca
  8 KB (1,246 words) - 21:58, 10 August 2020
• 2010 AMC 10B Problems/Problem 6
  ...h <math>\angle COB = 50^\circ</math>. What is the degree measure of <math>\angle CAB</math>? ...\cong \angle OAC</math>. They also sum to <math>50^{\circ}</math>, so each angle is <math>\boxed{\textbf{(B)}\ 25}</math>.
  2 KB (260 words) - 17:00, 1 August 2022
• 2010 AMC 10A Problems/Problem 7
  ...45 degrees. She then switches directions to southeast, meaning a 90 degree angle change. The distance now from traveling north for one mile, and her current
  3 KB (370 words) - 00:16, 29 June 2022
• Python reference
  Let's figure out the sine of a 30-degree angle in Python! ...tions f(g(x))). Take 30, convert it to radians, then take the sine of that angle.
  28 KB (4,762 words) - 21:20, 12 June 2023
• 1975 IMO Problems
  ...Q = 30^\circ, \angle ABR = \angle BAR = 15^\circ</math>. Prove that <math>\angle QRP = 90^\circ</math> and <math>QR = RP</math>. (that is, <math>P</math> is homogeneous of degree <math>n</math>),
  2 KB (416 words) - 16:06, 29 January 2021
• 2011 AMC 10B Problems/Problem 18
  ...<math>\angle AMD = \angle CMD</math>. What is the degree measure of <math>\angle AMD</math>? ...BMC = 30^{\circ}</math>. If we let <math>x</math> be the measure of <math>\angle AMD,</math> then
  5 KB (782 words) - 14:29, 1 April 2024
• 2011 AMC 12B Problems
  ...ths in the ratio <math>2 : 3</math>. What is the degree measure of <math>\angle{BAC}</math>? ...t <math>\angle AMD=\angle CMD</math>. What is the degree measure of <math>\angle AMD</math>?
  13 KB (1,978 words) - 16:28, 12 July 2020
• 2011 AMC 12B Problems/Problem 6
  ...ths in the ratio <math>2 : 3</math>. What is the degree measure of <math>\angle{BAC}</math>? ...er to solve this problem, use of the tangent-tangent intersection theorem (Angle of intersection between two tangents dividing a circle into arc length A an
  2 KB (370 words) - 13:35, 26 January 2021
• 2011 AIME II Problems/Problem 3
  ...sequence]] with integer values. Find the degree measure of the smallest [[angle]]. The average angle in an 18-gon is <math>160^\circ</math>. In an arithmetic sequence the avera
  3 KB (547 words) - 01:13, 31 January 2024
• 2011 AIME II Problems
  ...etic sequence with integer values. Find the degree measure of the smallest angle. ...C</math>, <math>AB=20</math> and <math>AC=11</math>. The angle bisector of angle <math>A</math> intersects <math>BC</math> at point <math>D</math>, and poin
  8 KB (1,301 words) - 08:43, 11 October 2020
• Tridecagon
  It has an internal angle degree of ~152.308 degrees.
  174 bytes (22 words) - 03:15, 24 September 2018
• 1999 AMC 8 Problems
  What is the degree measure of the smaller angle formed by the hands of a clock at 10 o clock? The degree measure of angle <math>A</math> is
  17 KB (2,394 words) - 19:51, 8 May 2023
• Mock Geometry AIME 2011 Problems
  ...uare, and let <math>AB_1C_1D_1</math> be its image after a <math>30</math> degree rotation about point <math>A.</math> The area of the region consisting of a ...lie on a plane, and their pairwise intersections meet at angles of integer degree. How many possible values are there for the smallest of these angles?
  8 KB (1,349 words) - 19:10, 14 June 2022
• 2011 AMC 10B Problems
  ...c}</math> larger than the other. What is the degree measure of the largest angle in the triangle? ...</math> are in the ratio <math>4 : 5</math>. What is the degree measure of angle <math>BCD</math>?
  13 KB (2,090 words) - 18:05, 7 January 2021
• 2011 AMC 10B Problems/Problem 7
  ...c}</math> larger than the other. What is the degree measure of the largest angle in the triangle? The sum of two angles in a triangle is <math>\frac{6}{5}</math> of a right angle <math>\longrightarrow \frac{6}{5} \times 90 = 108</math>
  1 KB (176 words) - 13:11, 4 July 2013
• 2011 AMC 10B Problems/Problem 9
  ...to twice the ratio of sides (in similar figures) because area is a second-degree property of similar figures. So like solution 3, the ratio of sides is <mat ...AA</math> similarity (<math>\angle B=\angle B</math> and <math>\angle EDB=\angle ACB</math>). Thus, let the side length of <math>ED</math> equal <math>3x</m
  4 KB (587 words) - 22:08, 31 August 2023
• 2011 AMC 10B Problems/Problem 17
  ...</math> are in the ratio <math>4 : 5</math>. What is the degree measure of angle <math>BCD</math>? ...gle sum theorem, <math>4x+5x+90=180 \longrightarrow x=10</math> and <math>\angle ABE = 50</math>.
  5 KB (699 words) - 04:53, 21 January 2023
• 2007 AMC 10B Problems
  ...nd <math>\angle AOB=140^\circ</math>. What is the degree measure of <math>\angle ABC?</math> ...\angle A= \angle B = 90^\circ.</math> What is the degree measure of <math>\angle E?</math>
  15 KB (2,297 words) - 12:57, 19 February 2020
• 2007 AMC 10B Problems/Problem 4
  ...angle AOB=140^\circ,</math> as shown. What is the degree measure of <math>\angle ABC?</math> Because all the [[central angle]]s of a circle add up to <math>360^\circ,</math>
  928 bytes (140 words) - 12:19, 4 July 2013
• 2007 AMC 10B Problems/Problem 7
  ...\angle A= \angle B = 90^\circ.</math> What is the degree measure of <math>\angle E?</math> ...iangle, <math>\angle AEC = 90</math> and <math>\angle CED = 60.</math> Use angle addition:
  1 KB (181 words) - 12:54, 4 June 2021
• 2007 AMC 10B Problems/Problem 15
  ...angle B=3 \angle C=4 \angle D.</math> What is the degree measure of <math>\angle A,</math> rounded to the nearest whole number? 360 &= \angle A + \angle B + \angle C + \angle D\\
  997 bytes (137 words) - 12:22, 4 July 2013
• 2011 AMC 12B Problems/Problem 10
  ...t <math>\angle AMD=\angle CMD</math>. What is the degree measure of <math>\angle AMD</math>? ...</math>. Therefore, <math>\angle BMC = 30^\circ</math>. Therefore <math>\angle AMD=\boxed{\mathrm{(E)}\ 75^\circ}</math>
  781 bytes (119 words) - 10:11, 5 August 2019
• 1999 AMC 8 Problems/Problem 2
  What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?
  1 KB (209 words) - 21:45, 15 January 2024
• 1999 AMC 8 Problems/Problem 21
  The degree measure of angle <math>A</math> is Angle-chasing using the small triangles:
  2 KB (332 words) - 22:27, 24 January 2024
• 2005 CEMC Gauss (Grade 7) Problems
  //put a label at the end of the 75 degree unit vector (and position it out 75 degrees) //put a label at the end of the 75 degree unit vector (rotate label 75 degrees to create a tick)
  16 KB (2,317 words) - 03:54, 24 October 2014
• 2010 PUMaC Problems
  ...h>AC = 5</math>, and <math>BC = 6</math>. An angle bisector is drawn from angle <math>A</math>, and meets <math>BC</math> at <math>M</math>. What is the n ...twice that of rectangle <math>AGPE</math>. Given that the value of <math>\angle FAH</math> in degrees is <math>x</math>, find the nearest integer to <math>
  22 KB (3,694 words) - 23:58, 3 June 2022
• 2009 PUMaC Problems
  Given that <math>P(x)</math> is the least degree polynomial with rational coefficients such that ...h>A</math> falls on line <math>EF</math>. How large, in degrees, is <math>\angle ABM</math>?
  25 KB (4,154 words) - 16:27, 2 September 2011
• 1985 AHSME Problems
  ...missing piece (the mouth) has central angle <math>\usepackage{gensymb} 60\degree</math>. What is the perimeter of the monster in cm? ...kage{gensymb} A = 20 \degree</math> and <math>\usepackage{gensymb} B = 25 \degree</math>, then the value of <math>\left(1+\tan A\right)\left(1+\tan B\right)<
  17 KB (2,488 words) - 03:26, 20 March 2024
• 1985 AHSME Problems/Problem 2
  ...missing piece (the mouth) has central angle <math>\usepackage{gensymb} 60\degree</math>. What is the perimeter of the monster in cm?
  1 KB (181 words) - 18:35, 19 March 2024
• 1985 AHSME Problems/Problem 16
  ...kage{gensymb} A = 20 \degree</math> and <math>\usepackage{gensymb} B = 25 \degree</math>, then the value of <math>\left(1+\tan A\right)\left(1+\tan B\right)< ...package{gensymb} 25 \degree + 20 \degree = 45 \degree</math>, we apply the angle sum formula <cmath>\tan(A+B) = \frac{\tan A+\tan B}{1-\tan A\tan B},</cmath
  5 KB (904 words) - 22:25, 19 March 2024
• Mock Geometry AIME 2011 Problems/Problem 1
  ...uare, and let <math>AB_1C_1D_1</math> be its image after a <math>30</math> degree rotation about point <math>A.</math> The area of the region consisting of a ...<math> \triangle AED_1\cong\triangle AEB </math>, since <math> \angle ABE=\angle AD_1E=90^\circ </math>, <math> AD_1=AB=1 </math>, and <math> AE=AE </math>,
  2 KB (376 words) - 22:06, 23 December 2022
• Mock Geometry AIME 2011 Problems/Problem 2
  ...lie on a plane, and their pairwise intersections meet at angles of integer degree. How many possible values are there for the smallest of these angles? ...es. One line can be translated across the plane, without rotation, and the angle between the two lines will remain the same.
  1 KB (174 words) - 22:06, 23 December 2022
• 2012 AMC 10A Problems/Problem 4
  ...20^\circ </math>. What is the smallest possible degree measure for <math>\angle CBD</math>? .../math> share ray <math>AB</math>. In order to minimize the value of <math>\angle CBD</math>, <math>D</math> should be located between <math>A</math> and <ma
  882 bytes (131 words) - 13:56, 1 July 2023
• 2012 AMC 10A Problems/Problem 10
  ...metic sequence. What is the degree measure of the smallest possible sector angle? ...>a_1+11d</math>, where <math>d</math> is the common difference. Since each angle measure must be an integer, <math>d</math> must also be an integer. We can
  4 KB (592 words) - 13:54, 1 July 2023
• 2012 AMC 10A Problems
  ...e ABD = 20^\circ </math>. What is the smallest possible degree measure for angle <math>CBD</math>? ...metic sequence. What is the degree measure of the smallest possible sector angle?
  13 KB (1,994 words) - 01:31, 22 December 2023
• 2012 AMC 12A Problems
  ...etic sequence. What is the degree measure of the smallest possible sector angle? ...that side of length <math>9</math>. Let <math>\theta</math> be the acute angle formed by that side and the median. What is <math>\sin{\theta}</math>?
  14 KB (2,197 words) - 13:34, 12 August 2020
• 1989 AHSME Problems/Problem 19
  ...a</math>, and <math>5\theta</math> for some <math>\theta</math>. By Circle Angle Sum, we obtain <math>3\theta+4\theta+5\theta=360</math>. Solving yields <ma ...cutting off length <math>4</math> is <math>60</math> degrees, and the last angle of the triangle is <math>75</math> degrees.
  4 KB (649 words) - 10:04, 20 May 2021
• 2012 AMC 12B Problems/Problem 15
  ...lar disk of radius 12, along 2 radii to form 2 sectors, one with a central angle of 120. He makes two circular cones using each sector to form the lateral s ...defined by the central angles, the smaller arc, a <math>120</math> degree angle, is half the size of the larger sector. so the smaller arc is <math>8\pi</m
  2 KB (259 words) - 13:42, 2 September 2020
• 2015 AIME I Problems
  ...gle AHG</math> by <math>12^\circ</math>. Find the degree measure of <math>\angle BAG</math>. Let <math>f(x)</math> be a third-degree polynomial with real coefficients satisfying
  10 KB (1,615 words) - 21:48, 13 January 2024
• 2012 AIME II Problems/Problem 13
  ...eta</math> be the measure of angle <math>BAD_1</math> (also the measure of angle <math>BAD_2</math>); by the Law of Cosines, Angle <math>E_1AC = E_1AD_1 + D_1AB + BAC = 60 + \theta + 60 = 120 + \theta</math
  13 KB (2,052 words) - 18:02, 5 February 2024
• 2006 IMO Problems
  ...or of the triangle satisfies <math>\angle PBA + \angle PCA = \angle PBC + \angle PCB</math>. Let <math>P(x)</math> be a polynomial of degree <math>n>1</math> with integer coefficients, and let <math>k</math> be a pos
  2 KB (402 words) - 23:18, 12 April 2021

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