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.
+2668 The sum of the angles is 180×(5−2)=540
The common difference is 60÷(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?
+2668 The sum of the angles is 180×(5−2)=540
The common difference is 60÷(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?
