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• Interior angle
  The '''interior angle''' is the [[angle]] between two line segments, having two endpoints connected via a path, facing the path connecting them. ...erior angles of an <math>n</math> sided regular polygon,are <math>180(1-{2\over n})</math> degrees.
  673 bytes (105 words) - 22:28, 27 February 2020
• 2003 AMC 10B Problems/Problem 19
  ...qquad\textbf{(D) } \frac{\pi +\sqrt{3}}{2} \qquad\textbf{(E) } \frac{7}{6}\pi - \frac{\sqrt{3}}{2}</math> ...n into <math>\frac{5}{6}</math> of a circle with radius <math>1</math> and two equilateral triangles with side length <math>1</math>.
  4 KB (606 words) - 13:19, 9 July 2021
• 1984 AHSME Problems/Problem 15
  This looks a lot like the formula relating the slopes of two [[perpendicular]] [[Line|lines]], which is <math> m_1\times m_2=-1 </math>, ...> 2x+3x=5x </math>, so <math> 5x=\frac{\pi}{2} </math> and <math> x=\frac{\pi}{10} </math>, or <math> 18^\circ, \boxed{\text{A}} </math>.
  3 KB (493 words) - 18:16, 4 June 2021
• 2009 AMC 8 Problems
  ...mbered sectors. What is the probability that the sum of the numbers in the two sectors is prime? draw((0,0)--(cos(pi/6),sin(pi/6)));
  18 KB (2,551 words) - 18:46, 27 February 2024
• 2000 AMC 8 Problems/Problem 19
  ...\ 10+5\pi\qquad\text{(C)}\ 50\qquad\text{(D)}\ 50+5\pi\qquad\text{(E)}\ 25\pi </math> Draw two squares: one that has opposing corners at <math>A</math> and <math>B</math
  2 KB (383 words) - 16:58, 12 January 2024
• 1995 AJHSME Problems/Problem 9
  ...angle. But <math>24</math> is too low, as it is less than the area of the two circles. Thus, the only reasonable answer is <math>\boxed{C}</math>, which
  2 KB (409 words) - 00:15, 5 July 2013
• 2008 AMC 8 Problems/Problem 18
  Two circles that share the same center have radii <math>10</math> meters and <m ...extbf{(C)}\ 10\pi+40\qquad\textbf{(D)}\ 20\pi+20\qquad \\ \textbf{(E)}\ 20\pi+40</math>
  2 KB (210 words) - 13:37, 19 October 2020
• 2010 AMC 8 Problems/Problem 23
  ...the center <math>O</math>. What is the ratio of the combined areas of the two semicircles to the area of circle <math>O</math>? ...ac{\sqrt 2}{4}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{\pi}\qquad\textbf{(D)}\ \frac{2}{3}\qquad\textbf{(E)}\ \frac{\sqrt 2}{2} </math
  2 KB (298 words) - 00:29, 18 December 2023
• 2009 AMC 8 Problems/Problem 12
  ...mbered sectors. What is the probability that the sum of the numbers in the two sectors is prime? draw((0,0)--(cos(pi/6),sin(pi/6)));
  1 KB (179 words) - 19:36, 15 April 2023
• 1979 USAMO Problems/Problem 4
  There are two ways to solve this problem. The first is more subtle, and the second is jus ...ngle POR,</math> and <math>b = \angle POQ.</math> Then <math>\angle ORP = \pi - x - a</math> and <math>\angle OQP = x - b.</math> Using the Law of Sines
  3 KB (568 words) - 12:24, 11 March 2018
• 1996 AHSME Problems
  ...-\pi\qquad\text{(C)}\ \frac{\pi} 2\qquad\text{(D)}\ \pi\qquad\text{(E)}\ 2\pi </math> Two opposite sides of a rectangle are each divided into <math>n</math> congruen
  15 KB (2,343 words) - 13:39, 19 February 2020
• 1992 AJHSME Problems/Problem 24
  ...e, which is <math>9\pi</math>. The area of the shaded region is <math>36-9\pi</math> which less than <math>36-9(3)=9</math>, closest to <math>\boxed{\tex
  1 KB (191 words) - 00:10, 5 July 2013
• 1950 AHSME Problems
  If the digit <math>1</math> is placed after a two digit number whose tens' digit is <math>t</math>, and units' digit is <math Two boys <math>A</math> and <math>B</math> start at the same time to ride from
  22 KB (3,306 words) - 19:50, 3 May 2023
• 1985 AHSME Problems
  ...qquad \mathrm{(D) \ } \frac{5}{6}\pi+2 \qquad \mathrm{(E) \ }\frac{5}{3}\pi+2 </math> ...h> unit apart both horizontally and vertically. A rubber band is stretched over <math>4</math> pegs as shown in the figure, forming a quadrilateral. Its ar
  17 KB (2,488 words) - 03:26, 20 March 2024
• 1985 AHSME Problems/Problem 2
  ...qquad \mathrm{(D) \ } \frac{5}{6}\pi+2 \qquad \mathrm{(E) \ }\frac{5}{3}\pi+2 </math> .... Hence the total perimeter in cm is <math>\boxed{\text{(E)} \ \frac{5}{3}\pi+2}</math>.
  1 KB (181 words) - 18:35, 19 March 2024
• 2010 AMC 8 Problems
  ...ath>16</math> feet higher than the top of another tree. The heights of the two trees are in the ratio <math>3:4</math>. In feet, how tall is the taller tr ...\pi} \qquad\textbf{(C)}\ \pi \qquad\textbf{(D)}\ 2\pi \qquad\textbf{(E)}\ \pi^{2}</math>
  18 KB (2,768 words) - 21:05, 9 January 2024
• 2011 AMC 8 Problems/Problem 25
  ...s closest to the ratio of the circle's shaded area to the area between the two squares? ...area of the smaller square subtracted from the area of the circle: <math>\pi - 2.</math>
  3 KB (511 words) - 07:47, 22 May 2023
• Mathtime Version 1 Issue 2
  ...r with a tight rope. The rope is tight so that there is no extra rope left over when bound around the four circles. If the radius of a circle is <math>5</m Two triangles are combined together with overlap so that the Star of David is f
  15 KB (2,444 words) - 21:46, 1 January 2012
• 1950 AHSME Problems/Problem 34
  ...qquad \textbf{(D)}\ \dfrac{5}{2\pi}\text{ in} \qquad \textbf{(E)}\ \dfrac{\pi}{5}\text{ in}</math> ...(or else the ratio of the circumference to the diameter wouldn't be <math>\pi</math> anymore)
  2 KB (313 words) - 22:24, 24 December 2023
• 1971 Canadian MO Problems/Problem 9
  Two flag poles of height <math>h</math> and <math>k</math> are situated <math>2 ...l Angles. In effect, we can construct our desired point P by reflecting H' over IJ and finding the intersection of H'K and IJ. Therefore, there is only one
  1 KB (204 words) - 18:09, 19 September 2012

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