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The interior angle measures of a pentagon form an arithmetic progression. The difference between the largest and smallest angle measures is 60 degrees. Find the measure of the smallest angle, in degrees.

 Jun 29, 2022

Best Answer 

 #1
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The sum of the angles is \(180 \times (5 - 2) = 540\)

 

The common difference is \(60 \div (5 - 1 ) = 15\)

 

Let x be the 3rd largest angle in the series. This gives: \((x - 30) + (x + 15) + (x) + (x - 15) + (x-30) = 540\)

 

Solving for x gives us \(x = 108\)


This means that the 3rd largest angle is 108 degrees. If this is the case, what is the smallest angle?

 Jun 29, 2022
 #1
avatar+2293 
+1
Best Answer

The sum of the angles is \(180 \times (5 - 2) = 540\)

 

The common difference is \(60 \div (5 - 1 ) = 15\)

 

Let x be the 3rd largest angle in the series. This gives: \((x - 30) + (x + 15) + (x) + (x - 15) + (x-30) = 540\)

 

Solving for x gives us \(x = 108\)


This means that the 3rd largest angle is 108 degrees. If this is the case, what is the smallest angle?

BuilderBoi Jun 29, 2022

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