Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.

Correct result:

x =  75 °

Solution:

A1=36012⋅ 1=30 ∘ A4=36012⋅ 4=120 ∘ A2=36012⋅ 2=60 ∘ A10=36012⋅ 10=300 ∘  s1=A4−A12=120−302=45 ∘ s2=A10−A22=300−602=120 ∘  x1=s2−s1=120−45=75 ∘ x2=180−x1=180−75=105 ∘  x=x1=75=75∘A_{1}=\dfrac{ 360 }{ 12 } \cdot \ 1=30 \ ^\circ \ \\ A_{4}=\dfrac{ 360 }{ 12 } \cdot \ 4=120 \ ^\circ \ \\ A_{2}=\dfrac{ 360 }{ 12 } \cdot \ 2=60 \ ^\circ \ \\ A_{10}=\dfrac{ 360 }{ 12 } \cdot \ 10=300 \ ^\circ \ \\ \ \\ s_{1}=\dfrac{ A_{4}-A_{1} }{ 2 }=\dfrac{ 120-30 }{ 2 }=45 \ ^\circ \ \\ s_{2}=\dfrac{ A_{10}-A_{2} }{ 2 }=\dfrac{ 300-60 }{ 2 }=120 \ ^\circ \ \\ \ \\ x_{1}=s_{2}-s_{1}=120-45=75 \ ^\circ \ \\ x_{2}=180 - x_{1}=180 - 75=105 \ ^\circ \ \\ \ \\ x=x_{1}=75=75 ^\circ

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  • Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  • Inscribed circle
    vpisana2 Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
  • Alfa, beta, gama
    angles_in_triangle In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
  • In a 2
    angles_7 In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
  • Candy - MO
    cukriky_4 Gretel deploys to the vertex of a regular octagon different numbers from one to eight candy. Peter can then choose which three piles of candy give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles trian
  • Regular n-gon
    10gon_polygon In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
  • Annulus
    annulus_inscribed_circles Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  • Circles
    circles How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
  • Trucks
    bricks Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks broug
  • Line
    skew_lines It is true that the lines that do not intersect are parallel?
  • Parametric equation
    line Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
  • Line
    img2 Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
  • Coordinates of vector
    vectors_2 Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?