The number of sides in a regular polygon is T times the number of di

Question

The number of sides in a regular polygon is ‘T’ times the number of diagonals in it. What is the interior angle of this polygon in terms of T?

A.  540*\frac{(T+2)}{(3T+2)}

B.  360*\frac{(T+2)}{(3T+2)}

C.  270*\frac{(T+2)}{(3T+2)}

D.  180*\frac{(T+2)}{(3T+2)}

E.  90*\frac{(T+2)}{(3T+2)}

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GMATinsight · Answer

CONCEPT : DIagonal in a Regular Polygon of n sides  = \frac{n*(n-3)}{2}

Hard but a good Question

Please find the step-by-stepsolution as attached below

Answer: Option D

https://www.youtube.com/watch?v=LhQrtu24Y0M

lacktutor · Answer

Let n be the number of sides of the regular polygon.

180\frac{( n-2)}{n} = 180 (1 - \frac{2}{n})=  ???

n = T * \frac{n(n-3)}{2} 
--->  2 = T (n -3 )

2= Tn - 3T

n = \frac{(3T+ 2)}{T}

180 ( 1- \frac{2}{ n} )= 180 (1- \frac{2T}{(3T+2)})= 180 \frac{(T+2)}{ (3T+2)}

Answer (D)

Kinshook · Answer

Given: The number of sides in a regular polygon is ‘T’ times the number of diagonals in it.

Asked: What is the interior angle of this polygon in terms of T?

Let the number of sides in a regular polygon be n

Number of diagonals =  ^nC_2 - n = \frac{n(n-1)}{2}- n = \frac{n(n-1-2)}{2} = \frac{n(n-3)}{2} = \frac{n}{T} 
 T= \frac{2}{(n-3)} 
 n = \frac{2}{T} + 3 = \frac{(3T+2)}{T} 
 n-2 = \frac{2}{T} + 1 = \frac{(T+2)}{T}

The interior angle of this polygon =  \frac{(n-2)180}{n} = \frac{180\frac{(T+2)}{T}}{\frac{(3T+2)}{T}} = \frac{180(T+2)}{(3T+2)}
 
IMO D

monk123 · Answer

Bunuel 
can we do this way ?
let t=2. & diagonals be 2. 
then, Sides=4.
it could be a square or a rectangle. we should aim for 90 degree angle.
putting the value of T in answer choices we get answer (D).

Fdambro294 · Answer

In a Regular Polygon, each Interior Angle and Each Exterior Angle (taken one time at each vertex) are EQUAL.

Each Exterior Angle of an N Sided Regular Polygon = 360 degrees / N-Sides

Each Interior Angle makes a Straight Line Angle with the Exterior Angle

thus, Each Interior Angle of an N Sided Regular Polygon = 180 - (360/N) = ?

This is what we need to find "in terms of T"

"the no. of sides in a regular polygon is "T" times the number of diagonals in it"

N = (T) *

Isolate N and solve in terms of T

2N = (T) *

----cancel an N Factor from each side----

2 = T * (N - 3)

2 = TN - 3T

3T + 2 = TN

N = (3T + 2)/T

----now plug this in for N into -----> 180 - (360/N)

180 - (360) /

180 -

---find common denominator for 180 ------> 180 * (3T + 2) / (3T + 2)

-

NUMERATOR = 180(3T + 2) - 360T

= 540T + 360 - 360T

= 180T + 360

DENOMINATOR = (3T + 2)

Answer:

(180T + 360) / (3T + 2)

180 * (T + 2) / (3T + 2)

(D)

adityasuresh · Answer

Here’s what I did I used the formula for calculating the no of diagonals:n*(n-3)/2. I assumed the no of sides to be 5, so the no of diagonals using the formula is 5*(5-3)/2 =5 so stem mentions t times so 5 is one time 5 so t=1 , an interior angle in a regular 5 sided figure =(5-2)*180 = 540,so each angle is 540/5 = 108

Plug in t =1 in option d it yields 108, 180*(1+2)/3+2 = 108

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Plug in t =1 in option d it yields 108, 180*(1+2)/3+2 = 108

The number of sides in a regular polygon is T times the number of di

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The number of sides in a regular polygon is T times the number of di

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards