Get premium membership and access questions with answers, video lessons as well as revision papers.

A regular polygon is such that its interior angle exceeds three times the exterior angle by 20^o. Find

A regular polygon is such that its interior angle exceeds three times the exterior angle by 20^o. Find the number of sides the polygon has.

Answers

Let interior angle be x.

exterior angle is (180 - x)^o

x = 3(180 - x) + 20

x = 540 + 20

4x = 540 + 20

4x = 560; x = 140

exterior angle

= (180^o - 140^o) = 40^o

the number of sides is

$\frac{360}{40}$ = 90 sides

---

johnmulu answered the question on June 12, 2017 at 06:40

Next: Where is salt mined in Kenya?
Previous: Where is Diatomite mined in Kenya?

View More Mathematics Questions and Answers | Return to Questions Index

Related Questions

• The ratio of the interior angle to the exterior angle of a regular polygon is 23:2. Find the number of sides the polygon has. (Solved)
  

  The ratio of the interior angle to the exterior angle of a regular polygon is 23:2. Find the number of sides the polygon has.

  Date posted: June 12, 2017.  Answers (1)

• The interior angle of a regular polygon exceeds the exterior by 144^o. Find the (Solved)
  

  The interior angle of a regular polygon exceeds the exterior by 144^o. Find the
  (a) number of sides
  (b) sum of interior angles

  Date posted: June 12, 2017.  Answers (1)

• Each interior angle of a regular polygon is 120^o larger than the exterior angle. Determine the number of sides the polygon has. (Solved)
  

  Each interior angle of a regular polygon is 120^o larger than the exterior angle. Determine the number of sides the polygon has.

  Date posted: June 12, 2017.  Answers (1)

• The size of each interior angle of a regular polygon is 5 times the size of the exterior angle. Find the number of sides of the polygon. (Solved)
  

  The size of each interior angle of a regular polygon is 5 times the size of the exterior angle. Find the number of sides of the polygon.

  Date posted: June 10, 2017.  Answers (1)

• If each interior angle of a regular polygon is x^o and each exterior angle is (Solved)
  

  If each interior angle of a regular polygon is $x^o$and each exterior angle is
  $\frac{x - 36}{3}$
  Calculate the sum of the interior angles in the polygon.

  Date posted: June 10, 2017.  Answers (1)

• A regular polygon has its interior angle as 156^o. Find the number of sides that the polygon has. (Solved)
  

  A regular polygon has its interior angle as 156^o. Find the number of sides that the polygon has.

  Date posted: June 10, 2017.  Answers (1)

• The sum of interior angles of a polygon is 2880^o. Find (Solved)
  

  The sum of interior angles of a polygon is 2880^o. Find
  (a) The number of sides the polygon has.
  (b) The number of triangles which can be formed when diagonals are drawn from one vertex connecting the other vertices.

  Date posted: June 9, 2017.  Answers (1)

• Two of the interior angles of a pentagon are 100^o and 140^o. Find the remaining angles if they are all equal. (Solved)
  

  Two of the interior angles of a pentagon are 100^o and 140^o. Find the remaining angles if they are all equal.

  Date posted: June 9, 2017.  Answers (1)

• The figure below shows part of a regular polygon not drawn to scale. (Solved)
  

  The figure below shows part of a regular polygon not drawn to scale.
  
  Determine the number of sides the polygon has.

  Date posted: June 9, 2017.  Answers (1)

• Find the sum of interior angles of a regular polygon with 18 sides. (Solved)
  

  Find the sum of interior angles of a regular polygon with 18 sides.

  Date posted: June 9, 2017.  Answers (1)

• The angles of a quadrilateral are 3x^o, 2x^o, (x+54)^o and 2(x-7)^o. Find the smallest angle of the polygon. (Solved)
  

  The angles of a quadrilateral are 3x^o, 2x^o, (x+54)^o and 2(x-7)^o. Find the smallest angle of the polygon.

  Date posted: June 9, 2017.  Answers (1)

• In the figure below AB is parallel to DE, angle ABD = 30^o and angle DCE = 70^o. Giving reasons, find angle:(Solved)
  

  In the figure below AB is parallel to DE, angle ABD = 30^o and angle DCE = 70^o. Giving reasons, find angle:
  (i) CDE
  (ii) CEF.
  

  Date posted: June 9, 2017.  Answers (1)

• In the figure below, ABCD is a cyclic quadrilateral and BD is diagonal. EADF is straight line, CDF = 68^o, BDC = 45^o and BAE = 98^o(Solved)
  

  In the figure below, ABCD is a cyclic quadrilateral and BD is diagonal. EADF is straight line, CDF = 68^o, BDC = 45^o and BAE = 98^o
  
  Calculate the size of
  (a) CBD (b) ABD

  Date posted: June 9, 2017.  Answers (1)

• In the figure below, AB is parallel to DE. DE bisectors angle BDG and DCF = 60^o and CFG = 110^o. (Solved)
  

  In the figure below, AB is parallel to DE. DE bisectors angle BDG and DCF = 60^o and CFG = 110^o.
  Find (a) CDF (b) ABD
  Give reasons for your answer.
  

  Date posted: June 9, 2017.  Answers (1)

• In the figure below, O is the centre of the circle and OAC = 38^o. Find (Solved)
  

  In the figure below, O is the centre of the circle and OAC = 38^o. Find

  Date posted: June 9, 2017.  Answers (1)

• Find the value of a and b in (Solved)
  

  Find the value of a and b in
  

  Date posted: June 9, 2017.  Answers (1)

• Find the value of x in the figure below. (Solved)
  

  Find the value of x in the figure below.
  

  Date posted: June 9, 2017.  Answers (1)

• Find the value of p and y in the figure below. (Solved)
  

  Find the value of p and y in the figure below.
  

  Date posted: June 9, 2017.  Answers (1)

• The opposite angle of a cyclic quadrilateral are (5x + 40)^o and (3x - 20)^o respectively. Find the difference between the two angles. (Solved)
  

  The opposite angle of a cyclic quadrilateral are (5x + 40)^o and (3x - 20)^o respectively. Find the difference between the two angles.

  Date posted: June 9, 2017.  Answers (1)

• The three angles of a triangle are (x-20)^o, (4x-15)^o and (2x+5)^o. Find the difference between the largest and the smallest. (Solved)
  

  The three angles of a triangle are (x-20)^o, (4x-15)^o and (2x+5)^o. Find the difference between the largest and the smallest.

  Date posted: June 9, 2017.  Answers (1)