n-gon

Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?

Correct result:

n =  6

Solution:

Sn=180(n−2)=70+1702n  n=360180−70+1702=6S_n = 180(n-2) = \dfrac{ 70 + 170} {2} n \ \\ \ \\ n = \dfrac{ 360}{180 - \dfrac{ 70 + 170} {2}} = 6

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

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:

  • Angles of a hexagon
    hexagon-irregular Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence and the smallest angle is 70°.
  • 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. .
  • Triangles
    triangles_6 Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
  • AS sequence
    AP In an arithmetic sequence is given the difference d = -3 and a71 = 455. a) Determine the value of a62 b) Determine the sum of 71 members.
  • Radians
    pi_text Convert 270° to radians. Write result as multiple of number π.
  • Outer angles
    triangle_1111_3 The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C?
  • Angles in a triangle
    fun The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
  • Angle
    rightTriangle Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
  • N-gon angles
    ngon2 What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
  • Inner angles
    triangle_1111 The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
  • Sequence
    arithmetic_seq In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
  • RWY
    SFO_map Calculate the opposite direction of the runway 13. Runways are named by a number between 01 and 36, which is generally one tenth of the azimuth of the runway's heading in degrees: a runway numbered 09 points east (90°), runway 18 is south (180°), runway 2
  • 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.
  • Internal angles
    mo-klm The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
  • Angle in RT
    triangles_10 Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions.
  • Rotary cone
    cone_3 The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
  • Bricks pyramid
    The_Great_Pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?