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Each of the interior angles of a regular polygon is 140°…

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Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?

A. 9

B. 8

C. 7

D. 5

QUICK ANSWER…

A

DETAILS…

If each of the interior angles of a regular polygon is 140°, the number of sides of the polygon will be = 9.

Sum of all the interior angle of a regular polygon of n sides nA⁰ = 180(n – 2)

Where n = number of sides,

A⁰ = one of the interior angles.

Thus, substituting, we have:

nA⁰ = 180(n – 2)

n × 140 = 180(n – 2)

140n = 180n – 360

140n – 180n = -360

-40n = – 360

n = 360/40 = 9 sides. 

Now for the right answer to the above question:

  1. Option A is correct.
  2. Option B is not correct.
  3. C is incorrect.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • Sum of all the interior angles in a regular polygon = 180(n – 2).
  • Sum of all the exterior angles of a regular polygon = 360.
  • If one of the interior angles of a regular polygon is A⁰, then n × A⁰ = 180(n – 2).
  • If one of the exterior angles of a regular polygon is B⁰, then n × B⁰ = 360.
  • n stands for the number of sides.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 19 /

1 Answers

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    Sum of all the interior angles in a regular polygon = 180(n – 2).

    Admin - Mar 28, 2022 | Reply


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