Interior Ratios

Geometry Level 1

Which of the following is the ratio of the measure of an interior angle of a 24-sided regular polygon to that of a 12-sided regular polygon?

11:10 2:1 11:5 3:1

3 solutions

Sandeep Bhardwaj
Aug 23, 2014

Each Interior angle of a Regular Polygon of $n$ sides = $\left( 180^{\circ}-\dfrac{360^{\circ}}{n} \right)$

Also,

Each Exterior angle of a Regular Polygon of $n$ sides = $\left(\dfrac{360^{\circ}}{n} \right)$

You are right

Hameed Rasaq - 1 year, 11 months ago

Mohammad Rahman
Nov 22, 2015

Something is wrong with the question. I think the comparison is not between 24 sides polygon and 12 side polygon, rather it is between 24 side polygon and 20 side polygon then the answer will be 11:10 otherwise there is no answer in the options as per the given situation.

to get the interior angle to a regular polygon one can start by calculating what the total sum of its interior angles will be and then divide it by the amount of angles, so for the 24 it will be (360 22)/24=330, and for the 12 it will be (360 10)/12=300 the factor between 330 and 300 is that of 11:10

Francisco Parente - 5 years, 6 months ago

"(360x22)/24=330" this is totally wrong you should write (180X22)/24=165

Bekzod Yusupov - 4 years, 1 month ago

Thanks for explaining! One could easily have the misconception that the answer is $(24 - 2 ) : (12 - 2 ) = 11:5$ . However, that is true only for the sum of interior angles. The actual ratio is $\frac { 24 - 2 } { 24 } : \frac{ 12 - 2 } { 12 } = 11 : 10$ .

Calvin Lin Staff - 5 years, 6 months ago

(24-2)/24 : (12-2)/12 = 11 : 10 isn't it? why is it 11 : 5 ?

Leonard Gratias Agamus - 5 years, 5 months ago

@Leonard Gratias Agamus – Ah thanks. I swapped the 2 ratios. Edited them.

Calvin Lin Staff - 5 years, 5 months ago

The question is correct

Hameed Rasaq - 1 year, 11 months ago

Ahmad Aboulsoud
Apr 2, 2015

substitute n = 24 into formula 180(n - 2)/n and n=12 into the formula 180(n-2) / n and devide them

Interior Ratios

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