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.
+2666 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?
+2666 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?
