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# polygon

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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

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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
+1

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