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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 e****ach 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:**

**Option A is correct.****Option B is not correct.****C is incorrect.****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 20****21**** JAMB-UTME**** MATHEMATICS**** question**** 19 ****/**