• Member
• Recent Posts

Admin

Latest posts by Admin (see all)

• Which of the following groups of physical properties increase from… - 02/05/2023
• Which of the following diagrams represents correctly an n-p-n transistor? - 02/05/2023
• 12.0g of a mixture of potassium carbonate and potassium chloride were - 02/05/2023

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.

If you love our answers, you can simply join our community and also provide answers like this, fellow learners like you will appreciate it.

/ culled from 2021 JAMB-UTME MATHEMATICS question 19 /